Content check — Elementary Algebra, Chapter 10: Quadratic Equations

Every problem in the chapter beside the book’s answer, a chapter at a time as you scroll.

Chapter 10: Quadratic Equations

294 problems · 32 figures

Be Prepared 10.1 §10.1 source ↗

Simplify:

\sqrt{75}

.
If you missed this problem, review Example 9.12.

Example 9.12 in the book ↗

Answer

5 \sqrt{3}

Be Prepared 10.2 §10.1 source ↗

Simplify:

\sqrt{\frac{64}{3}}

.
If you missed this problem, review Example 9.67.

Example 9.67 in the book ↗

Answer

\frac{8 \sqrt{3}}{3}

Be Prepared 10.3 §10.1 source ↗

Factor:

4 x^{2} - 12 x + 9

.
If you missed this problem, review Example 7.43.

Example 7.43 in the book ↗

Answer

{2 x - 3}^{2}

Try It 10.1 §10.1 source ↗

Solve:

x^{2} = 81

Answer

x = 9, x = −9

Try It 10.2 §10.1 source ↗

Solve:

y^{2} = 121

Answer

y = 11, y = −11

Try It 10.3 §10.1 source ↗

Solve:

x^{2} - 50 = 0

Answer

x = 5 \sqrt{2}, x = −5 \sqrt{2}

Try It 10.4 §10.1 source ↗

Solve:

y^{2} - 27 = 0

Answer

y = 3 \sqrt{3}, y = −3 \sqrt{3}

Try It 10.5 §10.1 source ↗

Solve:

2 x^{2} = 98

Answer

x = 7, x = −7

Try It 10.6 §10.1 source ↗

Solve:

3 z^{2} = 108

Answer

z = 6, z = −6

Try It 10.7 §10.1 source ↗

Solve:

c^{2} + 12 = 0

Answer

no real solution

Try It 10.8 §10.1 source ↗

Solve:

d^{2} + 81 = 0

Answer

no real solution

Try It 10.9 §10.1 source ↗

Solve:

\frac{1}{2} x^{2} + 4 = 24

Answer

x =

2 \sqrt{10},

x =

−2 \sqrt{10}

Try It 10.10 §10.1 source ↗

Solve:

\frac{3}{4} y^{2} - 3 = 18

Answer

y = 2 \sqrt{7}, y = −2 \sqrt{7}

Try It 10.11 §10.1 source ↗

Solve:

5 r^{2} - 2 = 34

Answer

r =

\frac{6 \sqrt{5}}{5},

r =

-

\frac{6 \sqrt{5}}{5}

Try It 10.12 §10.1 source ↗

Solve:

3 t^{2} + 6 = 70

Answer

t =

\frac{8 \sqrt{3}}{3},

t =

-

\frac{8 \sqrt{3}}{3}

Try It 10.13 §10.1 source ↗

Solve:

{(q + 5)}^{2} = 1

Answer

q = −6, q = −4

Try It 10.14 §10.1 source ↗

Solve:

{(r - 3)}^{2} = 25

Answer

r = 8, r = −2

Try It 10.15 §10.1 source ↗

Solve:

{(a - 3)}^{2} = 18

Answer

a =

3 +

3 \sqrt{2},

a =

3 -

3 \sqrt{2}

Try It 10.16 §10.1 source ↗

Solve:

{(b + 2)}^{2} = 40

Answer

b =

−2 +

2 \sqrt{10},

b =

−2 -

2 \sqrt{10}

Try It 10.17 §10.1 source ↗

Solve:

{(x - \frac{1}{3})}^{2} = \frac{5}{9} .

Answer

x =

\frac{1}{3} +

\frac{\sqrt{5}}{3},

x =

\frac{1}{3} -

\frac{\sqrt{5}}{3}

Try It 10.18 §10.1 source ↗

Solve:

{(y - \frac{3}{4})}^{2} =

\frac{7}{16} .

Answer

y =

\frac{3}{4} +

\frac{\sqrt{7}}{4},

y =

\frac{3}{4} -

\frac{\sqrt{7}}{4}

Try It 10.19 §10.1 source ↗

Solve:

{(a - 5)}^{2} + 4 = 24

Answer

a =

5 +

2 \sqrt{5},

a =

5 -

2 \sqrt{5}

Try It 10.20 §10.1 source ↗

Solve:

{(b - 3)}^{2} - 8 = 24

Answer

b =

3 +

4 \sqrt{2},

b =

3 -

4 \sqrt{2}

Try It 10.21 §10.1 source ↗

Solve:

{(3 r + 4)}^{2} = −8

Answer

no real solution

Try It 10.22 §10.1 source ↗

Solve:

{(2 t - 8)}^{2} = −10

Answer

no real solution

Try It 10.23 §10.1 source ↗

Solve:

x^{2} - 6 x + 9 = 12

Answer

x =

3 +

2 \sqrt{3},

x =

3 -

2 \sqrt{3}

Try It 10.24 §10.1 source ↗

Solve:

y^{2} +

12 y +

36 =

32

Answer

y =

−6 +

4 \sqrt{2},

y =

−6 -

4 \sqrt{2}

Try It 10.25 §10.1 source ↗

Solve:

9 m^{2} -

12 m +

4 =

25

Answer

m = - 1, m = \frac{7}{3}

Try It 10.26 §10.1 source ↗

Solve:

16 n^{2} +

40 n +

25 =

4

Answer

n = - \frac{3}{4}, n = - \frac{7}{4}

10.1-1 §10.1 source ↗

Solve Quadratic Equations of the form $a x^{2} = k$ Using the Square Root Property

In the following exercises, solve the following quadratic equations.

$a^{2} = 49$

Answer

a = \pm 7

10.1-3 §10.1 source ↗

Solve Quadratic Equations of the form $a x^{2} = k$ Using the Square Root Property

In the following exercises, solve the following quadratic equations.

$r^{2} - 24 = 0$

Answer

r = \pm 2 \sqrt{6}

10.1-5 §10.1 source ↗

Solve Quadratic Equations of the form $a x^{2} = k$ Using the Square Root Property

In the following exercises, solve the following quadratic equations.

$u^{2} - 300 = 0$

Answer

u = \pm 10 \sqrt{3}

10.1-7 §10.1 source ↗

Solve Quadratic Equations of the form $a x^{2} = k$ Using the Square Root Property

In the following exercises, solve the following quadratic equations.

$4 m^{2} = 36$

Answer

m = \pm 3

10.1-9 §10.1 source ↗

Solve Quadratic Equations of the form $a x^{2} = k$ Using the Square Root Property

In the following exercises, solve the following quadratic equations.

$x^{2} + 20 = 0$

Answer

no real solution

10.1-11 §10.1 source ↗

Solve Quadratic Equations of the form $a x^{2} = k$ Using the Square Root Property

In the following exercises, solve the following quadratic equations.

$\frac{2}{5} a^{2} + 3 = 11$

Answer

a = \pm 2 \sqrt{5}

10.1-13 §10.1 source ↗

Solve Quadratic Equations of the form $a x^{2} = k$ Using the Square Root Property

In the following exercises, solve the following quadratic equations.

$7 p^{2} + 10 = 26$

Answer

p = \pm \frac{4 \sqrt{7}}{7}

10.1-15 §10.1 source ↗

Solve Quadratic Equations of the Form $a {(x - h)}^{2} = k$ Using the Square Root Property

In the following exercises, solve the following quadratic equations.

${(x + 2)}^{2} = 9$

Answer

x = 1, x = −5

10.1-17 §10.1 source ↗

Solve Quadratic Equations of the Form $a {(x - h)}^{2} = k$ Using the Square Root Property

In the following exercises, solve the following quadratic equations.

${(u - 6)}^{2} = 64$

Answer

u = 14, u = −2

10.1-19 §10.1 source ↗

Solve Quadratic Equations of the Form $a {(x - h)}^{2} = k$ Using the Square Root Property

In the following exercises, solve the following quadratic equations.

${(m - 6)}^{2} = 20$

Answer

m = 6 \pm 2 \sqrt{5}

10.1-21 §10.1 source ↗

Solve Quadratic Equations of the Form $a {(x - h)}^{2} = k$ Using the Square Root Property

In the following exercises, solve the following quadratic equations.

${(r - \frac{1}{2})}^{2} = \frac{3}{4}$

Answer

r = \frac{1}{2} \pm \frac{\sqrt{3}}{2}

10.1-23 §10.1 source ↗

Solve Quadratic Equations of the Form $a {(x - h)}^{2} = k$ Using the Square Root Property

In the following exercises, solve the following quadratic equations.

${(a - 7)}^{2} + 5 = 55$

Answer

a = 7 \pm 5 \sqrt{2}

10.1-25 §10.1 source ↗

Solve Quadratic Equations of the Form $a {(x - h)}^{2} = k$ Using the Square Root Property

In the following exercises, solve the following quadratic equations.

${(5 c + 1)}^{2} = −27$

Answer

no real solution

10.1-27 §10.1 source ↗

Solve Quadratic Equations of the Form $a {(x - h)}^{2} = k$ Using the Square Root Property

In the following exercises, solve the following quadratic equations.

$m^{2} - 4 m + 4 = 8$

Answer

m = 2 \pm 2 \sqrt{2}

10.1-29 §10.1 source ↗

Solve Quadratic Equations of the Form $a {(x - h)}^{2} = k$ Using the Square Root Property

In the following exercises, solve the following quadratic equations.

$25 x^{2} -$ $30 x +$ $9 =$ $36$

Answer

x = - \frac{3}{5}, x = \frac{9}{5}

10.1-31 §10.1 source ↗

Mixed Practice

In the following exercises, solve using the Square Root Property.

$2 r^{2} = 32$

Answer

r = \pm 4

10.1-33 §10.1 source ↗

Mixed Practice

In the following exercises, solve using the Square Root Property.

${(a - 4)}^{2} = 28$

Answer

a = 4 \pm 2 \sqrt{7}

10.1-35 §10.1 source ↗

Mixed Practice

In the following exercises, solve using the Square Root Property.

$9 w^{2} -$ $24 w +$ $16 =$ $1$

Answer

w = 1, w = \frac{5}{3}

10.1-37 §10.1 source ↗

Mixed Practice

In the following exercises, solve using the Square Root Property.

$a^{2} - 18 = 0$

Answer

a = \pm 3 \sqrt{2}

10.1-39 §10.1 source ↗

Mixed Practice

In the following exercises, solve using the Square Root Property.

${(p - \frac{1}{3})}^{2} = \frac{7}{9}$

Answer

p = \frac{1}{3} \pm \frac{\sqrt{7}}{3}

10.1-41 §10.1 source ↗

Mixed Practice

In the following exercises, solve using the Square Root Property.

$m^{2} + 12 = 0$

Answer

no real solution

10.1-43 §10.1 source ↗

Mixed Practice

In the following exercises, solve using the Square Root Property.

$u^{2} -$ $14 u +$ $49 =$ $72$

Answer

u = 7 \pm 6 \sqrt{2}

10.1-45 §10.1 source ↗

Mixed Practice

In the following exercises, solve using the Square Root Property.

${(m - 4)}^{2} + 3 = 15$

Answer

m = 4 \pm 2 \sqrt{3}

10.1-47 §10.1 source ↗

Mixed Practice

In the following exercises, solve using the Square Root Property.

${(x + 5)}^{2} = 4$

Answer

x = −3, x = −7

10.1-49 §10.1 source ↗

Mixed Practice

In the following exercises, solve using the Square Root Property.

$6 c^{2} + 4 = 29$

Answer

c = \pm \frac{5 \sqrt{6}}{6}

10.1-51 §10.1 source ↗

Mixed Practice

In the following exercises, solve using the Square Root Property.

${(x - 6)}^{2} + 7 = 3$

Answer

no real solution

10.1-53 §10.1 source ↗

Mixed Practice

In the following exercises, solve using the Square Root Property.

Paola has enough mulch to cover 48 square feet. She wants to use it to make three square vegetable gardens of equal sizes. Solve the equation $3 s^{2} = 48$ to find $s$ , the length of each garden side.

Answer

4 feet

10.1-55 §10.1 source ↗

Mixed Practice

In the following exercises, solve using the Square Root Property.

Explain why the equation $x^{2} + 12 = 8$ has no solution.

Answer

Answers will vary.

Be Prepared 10.4 §10.2 source ↗

Simplify

{(x + 12)}^{2}

.
If you missed this problem, review Example 6.47.

Example 6.47 View it in the book ↗

Answer

x^{2} + 24 x + 144

Be Prepared 10.5 §10.2 source ↗

Factor

y^{2} - 18 y + 81

.
If you missed this problem, review Example 7.42.

Example 7.42 in the book ↗

Answer

y - 9^{2}

Be Prepared 10.6 §10.2 source ↗

Factor

5 n^{2} + 40 n + 80

.
If you missed this problem, review Example 7.46.

Example 7.46 in the book ↗

Answer

5 (n + 4)^{2}

Try It 10.27 §10.2 source ↗

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$y^{2} + 12 y$

Answer

{(y + 6)}^{2}

Try It 10.28 §10.2 source ↗

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$z^{2} + 8 z$

Answer

{(z + 4)}^{2}

Try It 10.29 §10.2 source ↗

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$a^{2} - 20 a$

Answer

{(a - 10)}^{2}

Try It 10.30 §10.2 source ↗

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$b^{2} - 4 b$

Answer

{(b - 2)}^{2}

Try It 10.31 §10.2 source ↗

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$m^{2} - 5 m$

Answer

{(m - \frac{5}{2})}^{2}

Try It 10.32 §10.2 source ↗

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$n^{2} + 13 n$

Answer

{(n + \frac{13}{2})}^{2}

Try It 10.33 §10.2 source ↗

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$p^{2} + \frac{1}{4} p$

Answer

{(p + \frac{1}{8})}^{2}

Try It 10.34 §10.2 source ↗

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$q^{2} - \frac{2}{3} q$

Answer

{(q - \frac{1}{3})}^{2}

Try It 10.35 §10.2 source ↗

Solve

c^{2} + 4 c = 5

by completing the square.

Answer

c = −5, c = 1

Try It 10.36 §10.2 source ↗

Solve

d^{2} + 10 d = −9

by completing the square.

Answer

d = −9, d = −1

Try It 10.37 §10.2 source ↗

Solve

r^{2} - 4 r = 12

by completing the square.

Answer

r = −2, r = 6

Try It 10.38 §10.2 source ↗

Solve

t^{2} - 10 t = 11

by completing the square.

Answer

t = −1, t = 11

Try It 10.39 §10.2 source ↗

Solve

y^{2} - 10 y = −35

by completing the square.

Answer

no real solution

Try It 10.40 §10.2 source ↗

Solve

z^{2} + 8 z = −19

by completing the square.

Answer

no real solution

Try It 10.41 §10.2 source ↗

Solve

x^{2} - 16 x = −16

by completing the square.

Answer

x = 8 \pm 4 \sqrt{3}

Try It 10.42 §10.2 source ↗

Solve

y^{2} + 8 y = 11

by completing the square.

Answer

y = −4 \pm 3 \sqrt{3}

Try It 10.43 §10.2 source ↗

Solve

a^{2} + 4 a + 9 = 30

by completing the square.

Answer

a = −7, a = 3

Try It 10.44 §10.2 source ↗

Solve

b^{2} + 8 b - 4 = 16

by completing the square.

Answer

b = −10, b = 2

Try It 10.45 §10.2 source ↗

Solve

p^{2} = 5 p + 9

by completing the square.

Answer

p = \frac{5}{2} \pm \frac{\sqrt{61}}{2}

Try It 10.46 §10.2 source ↗

Solve

q^{2} = 7 q - 3

by completing the square.

Answer

q = \frac{7}{2} \pm \frac{\sqrt{37}}{2}

Try It 10.47 §10.2 source ↗

Solve

(c - 2) (c + 8) =

7

by completing the square.

Answer

c = −3 \pm 4 \sqrt{2}

Try It 10.48 §10.2 source ↗

Solve

(d - 7) (d + 3) =

56

by completing the square.

Answer

d = −7, d = 11

Try It 10.49 §10.2 source ↗

Solve

2 m^{2} + 16 m - 8 = 0

by completing the square.

Answer

m = −4 \pm 2 \sqrt{5}

Try It 10.50 §10.2 source ↗

Solve

4 n^{2} -

24 n -

56 =

8

by completing the square.

Answer

n = −2, 8

Try It 10.51 §10.2 source ↗

Solve

3 r^{2} - 2 r = 21

by completing the square.

Answer

r = - \frac{7}{3}, r = 3

Try It 10.52 §10.2 source ↗

Solve

4 t^{2} + 2 t = 20

by completing the square.

Answer

t = - \frac{5}{2}, t = 2

Try It 10.53 §10.2 source ↗

Solve

4 x^{2} + 3 x = 12

by completing the square.

Answer

x = - \frac{3}{8} \pm \frac{\sqrt{201}}{8}

Try It 10.54 §10.2 source ↗

Solve

5 y^{2} + 3 y = 10

by completing the square.

Answer

y =

-

\frac{3}{10} \pm \frac{\sqrt{209}}{10}

10.2-57 §10.2 source ↗

Complete the Square of a Binomial Expression

In the following exercises, complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.

$a^{2} + 10 a$

Answer

{(a + 5)}^{2}

10.2-59 §10.2 source ↗

Complete the Square of a Binomial Expression

In the following exercises, complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.

$m^{2} + 18 m$

Answer

{(m + 9)}^{2}

10.2-61 §10.2 source ↗

Complete the Square of a Binomial Expression

In the following exercises, complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.

$m^{2} - 24 m$

Answer

{(m - 12)}^{2}

10.2-63 §10.2 source ↗

Complete the Square of a Binomial Expression

In the following exercises, complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.

$p^{2} - 22 p$

Answer

{(p - 11)}^{2}

10.2-65 §10.2 source ↗

Complete the Square of a Binomial Expression

In the following exercises, complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.

$x^{2} - 9 x$

Answer

{(x - \frac{9}{2})}^{2}

10.2-67 §10.2 source ↗

Complete the Square of a Binomial Expression

In the following exercises, complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.

$p^{2} - \frac{1}{3} p$

Answer

{(p - \frac{1}{6})}^{2}

10.2-69 §10.2 source ↗

Solve Quadratic Equations of the Form $x^{2} + b x + c = 0$ by Completing the Square

In the following exercises, solve by completing the square.

$v^{2} + 6 v = 40$

Answer

v = −10, v = 4

10.2-71 §10.2 source ↗

Solve Quadratic Equations of the Form $x^{2} + b x + c = 0$ by Completing the Square

In the following exercises, solve by completing the square.

$u^{2} + 2 u = 3$

Answer

u = −3, u = 1

10.2-73 §10.2 source ↗

Solve Quadratic Equations of the Form $x^{2} + b x + c = 0$ by Completing the Square

In the following exercises, solve by completing the square.

$c^{2} - 12 c = 13$

Answer

c = −1, c = 13

10.2-75 §10.2 source ↗

Solve Quadratic Equations of the Form $x^{2} + b x + c = 0$ by Completing the Square

In the following exercises, solve by completing the square.

$x^{2} - 20 x = 21$

Answer

x = −1, x = 21

10.2-77 §10.2 source ↗

Solve Quadratic Equations of the Form $x^{2} + b x + c = 0$ by Completing the Square

In the following exercises, solve by completing the square.

$m^{2} + 4 m = −44$

Answer

no real solution

10.2-79 §10.2 source ↗

Solve Quadratic Equations of the Form $x^{2} + b x + c = 0$ by Completing the Square

In the following exercises, solve by completing the square.

$r^{2} + 6 r = −11$

Answer

no real solution

10.2-81 §10.2 source ↗

Solve Quadratic Equations of the Form $x^{2} + b x + c = 0$ by Completing the Square

In the following exercises, solve by completing the square.

$a^{2} - 10 a = −5$

Answer

a = 5 \pm 2 \sqrt{5}

10.2-83 §10.2 source ↗

Solve Quadratic Equations of the Form $x^{2} + b x + c = 0$ by Completing the Square

In the following exercises, solve by completing the square.

$u^{2} -$ $14 u +$ $12 =$ $−1$

Answer

u = 1, u = 13

10.2-85 §10.2 source ↗

Solve Quadratic Equations of the Form $x^{2} + b x + c = 0$ by Completing the Square

In the following exercises, solve by completing the square.

$v^{2} = 9 v + 2$

Answer

v = \frac{9}{2} \pm \frac{\sqrt{89}}{2}

10.2-87 §10.2 source ↗

Solve Quadratic Equations of the Form $x^{2} + b x + c = 0$ by Completing the Square

In the following exercises, solve by completing the square.

$(x + 6) (x - 2) =$ $9$

Answer

x = −7, x = 3

10.2-89 §10.2 source ↗

Solve Quadratic Equations of the Form $a x^{2} + b x + c = 0$ by Completing the Square

In the following exercises, solve by completing the square.

$3 m^{2} +$ $30 m -$ $27 =$ $6$

Answer

m = −11, m = 1

10.2-91 §10.2 source ↗

Solve Quadratic Equations of the Form $a x^{2} + b x + c = 0$ by Completing the Square

In the following exercises, solve by completing the square.

$2 c^{2} + c = 6$

Answer

c = −2, c = \frac{3}{2}

10.2-93 §10.2 source ↗

Solve Quadratic Equations of the Form $a x^{2} + b x + c = 0$ by Completing the Square

In the following exercises, solve by completing the square.

$2 p^{2} + 7 p = 14$

Answer

p = - \frac{7}{4} \pm \frac{\sqrt{161}}{4}

10.2-95 §10.2 source ↗

Solve Quadratic Equations of the Form $a x^{2} + b x + c = 0$ by Completing the Square

In the following exercises, solve by completing the square.

Rafi is designing a rectangular playground to have an area of 320 square feet. He wants one side of the playground to be four feet longer than the other side. Solve the equation $p^{2} + 4 p = 320$ for $p$ , the length of one side of the playground. What is the length of the other side?

Answer

16 feet, 20 feet

10.2-97 §10.2 source ↗

Solve Quadratic Equations of the Form $a x^{2} + b x + c = 0$ by Completing the Square

In the following exercises, solve by completing the square.

Solve the equation $x^{2} + 10 x = −25$ ⓐ by using the Square Root Property and ⓑ by completing the square. ⓒ Which method do you prefer? Why?

Answer

ⓐ

−5

ⓑ

−5

Be Prepared 10.7 §10.3 source ↗

Simplify:

\frac{−20 - 5}{10}

.
If you missed this problem, review Example 1.74.

Example 1.74 in the book ↗

Answer

- \frac{5}{2}

Be Prepared 10.8 §10.3 source ↗

Simplify:

4 + \sqrt{121}

.
If you missed this problem, review Example 9.29.

Example 9.29 in the book ↗

Answer

15

Be Prepared 10.9 §10.3 source ↗

Simplify:

\sqrt{128}

.
If you missed this problem, review Example 9.12.

Example 9.12 in the book ↗

Answer

8 \sqrt{2}

Try It 10.55 §10.3 source ↗

Solve

3 y^{2} - 5 y + 2 = 0

by using the Quadratic Formula.

Answer

y = \frac{2}{3}, y = 1

Try It 10.56 §10.3 source ↗

Solve

4 z^{2} + 2 z - 6 = 0

by using the Quadratic Formula.

Answer

z = - \frac{3}{2}, z = 1

Try It 10.57 §10.3 source ↗

Solve

a^{2} - 2 a - 15 = 0

by using the Quadratic Formula.

Answer

a = −3, a = 5

Try It 10.58 §10.3 source ↗

Solve

b^{2} + 10 b + 24 = 0

by using the Quadratic Formula.

Answer

b = −6, b = −4

Try It 10.59 §10.3 source ↗

Solve

2 p^{2} + 8 p + 5 = 0

by using the Quadratic Formula.

Answer

p = \frac{−4 \pm \sqrt{6}}{2}

Try It 10.60 §10.3 source ↗

Solve

5 q^{2} - 11 q + 3 = 0

by using the Quadratic Formula.

Answer

q = \frac{11 \pm \sqrt{61}}{10}

Try It 10.61 §10.3 source ↗

Solve

3 m^{2} + 12 m + 7 = 0

by using the Quadratic Formula.

Answer

m = \frac{−6 \pm \sqrt{15}}{3}

Try It 10.62 §10.3 source ↗

Solve

5 n^{2} + 4 n - 4 = 0

by using the Quadratic Formula.

Answer

n = \frac{−2 \pm 2 \sqrt{6}}{5}

Try It 10.63 §10.3 source ↗

Solve

4 a^{2} - 3 a + 8 = 0

by using the Quadratic Formula.

Answer

no real solution

Try It 10.64 §10.3 source ↗

Solve

5 b^{2} + 2 b + 4 = 0

by using the Quadratic Formula.

Answer

no real solution

Try It 10.65 §10.3 source ↗

Solve

x (x + 2) - 5 = 0

by using the Quadratic Formula.

Answer

x = −1 \pm \sqrt{6}

Try It 10.66 §10.3 source ↗

Solve

y (3 y - 1) - 2 = 0

by using the Quadratic Formula.

Answer

y = - \frac{2}{3}, y = 1

Try It 10.67 §10.3 source ↗

Solve

\frac{1}{4} c^{2} -

\frac{1}{3} c =

\frac{1}{12}

by using the Quadratic Formula.

Answer

c = \frac{2 \pm \sqrt{7}}{3}

Try It 10.68 §10.3 source ↗

Solve

\frac{1}{9} d^{2} -

\frac{1}{2} d =

-

\frac{1}{2}

by using the Quadratic Formula.

Answer

d = 3, d = \frac{3}{2}

Try It 10.69 §10.3 source ↗

Solve

r^{2} + 10 r + 25 = 0

by using the Quadratic Formula.

Answer

r = −5

Try It 10.70 §10.3 source ↗

Solve

25 t^{2} -

40 t =

−16

by using the Quadratic Formula.

Answer

t = \frac{4}{5}

Try It 10.71 §10.3 source ↗

Determine the number of solutions to each quadratic equation:

ⓐ $8 m^{2} - 3 m + 6 = 0$ ⓑ $5 z^{2} + 6 z - 2 = 0$ ⓒ $9 w^{2} +$ $24 w +$ $16 =$ $0$ ⓓ $9 u^{2} - 2 u + 4 = 0$

Answer

ⓐ no real solutions ⓑ 2 ⓒ 1 ⓓ no real solutions

Try It 10.72 §10.3 source ↗

Determine the number of solutions to each quadratic equation:

ⓐ $b^{2} + 7 b - 13 = 0$ ⓑ $5 a^{2} - 6 a + 10 = 0$ ⓒ $4 r^{2} -$ $20 r +$ $25 =$ $0$ ⓓ $7 t^{2} - 11 t + 3 = 0$

Answer

ⓐ 2 ⓑ no real solutions ⓒ 1 ⓓ 2

Try It 10.73 §10.3 source ↗

Identify the most appropriate method to use to solve each quadratic equation:

ⓐ $x^{2} + 6 x + 8 = 0$ ⓑ ${(n - 3)}^{2} = 16$ ⓒ $5 p^{2} - 6 p = 9$

Answer

ⓐ factor ⓑ Square Root Property ⓒ Quadratic Formula

Try It 10.74 §10.3 source ↗

Identify the most appropriate method to use to solve each quadratic equation:

ⓐ $8 a^{2} + 3 a - 9 = 0$ ⓑ $4 b^{2} + 4 b + 1 = 0$ ⓒ $5 c^{2} = 125$

Answer

ⓐ Quadratic Formula ⓑ factoring ⓒ Square Root Property

10.3-99 §10.3 source ↗

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$4 m^{2} + m - 3 = 0$

Answer

m = −1, m = \frac{3}{4}

10.3-101 §10.3 source ↗

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$2 p^{2} - 7 p + 3 = 0$

Answer

p = \frac{1}{2}, p = 3

10.3-103 §10.3 source ↗

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$p^{2} + 7 p + 12 = 0$

Answer

p = −4, p = −3

10.3-105 §10.3 source ↗

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$r^{2} - 8 r - 33 = 0$

Answer

r = −3, r = 11

10.3-107 §10.3 source ↗

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$3 u^{2} + 7 u - 2 = 0$

Answer

u = \frac{−7 \pm \sqrt{73}}{6}

10.3-109 §10.3 source ↗

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$2 a^{2} - 6 a + 3 = 0$

Answer

a = \frac{3 \pm \sqrt{3}}{2}

10.3-111 §10.3 source ↗

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$2 x^{2} + 3 x + 9 = 0$

Answer

no real solution

10.3-113 §10.3 source ↗

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$v (v + 5) - 10 = 0$

Answer

v = \frac{−5 \pm \sqrt{65}}{2}

10.3-115 §10.3 source ↗

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$\frac{1}{3} m^{2} +$ $\frac{1}{12} m =$ $\frac{1}{4}$

Answer

m = −1, m = \frac{3}{4}

10.3-117 §10.3 source ↗

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$16 c^{2} +$ $24 c +$ $9 =$ $0$

Answer

c = - \frac{3}{4}

10.3-119 §10.3 source ↗

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$5 m^{2} + 2 m - 7 = 0$

Answer

m = - \frac{7}{5}, m = 1

10.3-121 §10.3 source ↗

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$p^{2} - 6 p - 27 = 0$

Answer

p = −3, p = 9

10.3-123 §10.3 source ↗

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$4 r^{2} + 3 r - 5 = 0$

Answer

r = \frac{−3 \pm \sqrt{89}}{8}

10.3-125 §10.3 source ↗

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$2 a^{2} + 12 a + 5 = 0$

Answer

a = \frac{−6 \pm \sqrt{26}}{2}

10.3-127 §10.3 source ↗

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$\frac{3}{4} b^{2} + \frac{1}{2} b = \frac{3}{8}$

Answer

b = \frac{−2 \pm \sqrt{22}}{6}

10.3-129 §10.3 source ↗

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$2 x^{2} + 12 x - 3 = 0$

Answer

x = \frac{−6 \pm \sqrt{42}}{4}

10.3-131 §10.3 source ↗

Use the Discriminant to Predict the Number of Solutions of a Quadratic Equation

In the following exercises, determine the number of solutions to each quadratic equation.

ⓐ $4 x^{2} - 5 x + 16 = 0$

ⓑ $36 y^{2} +$ $36 y +$ $9 =$ $0$

ⓓ $18 n^{2} - 7 n + 3 = 0$

Answer

ⓐ no real solutions ⓑ 1
ⓒ 2 ⓓ no real solutions

10.3-133 §10.3 source ↗

Use the Discriminant to Predict the Number of Solutions of a Quadratic Equation

In the following exercises, determine the number of solutions to each quadratic equation.

ⓐ $r^{2} + 12 r + 36 = 0$

ⓑ $8 t^{2} - 11 t + 5 = 0$

ⓓ $3 v^{2} - 5 v - 1 = 0$

Answer

ⓐ 1 ⓑ no real solutions
ⓒ 1 ⓓ 2

10.3-135 §10.3 source ↗

Identify the Most Appropriate Method to Use to Solve a Quadratic Equation

In the following exercises, identify the most appropriate method (Factoring, Square Root, or Quadratic Formula) to use to solve each quadratic equation. Do not solve.

ⓐ $x^{2} - 5 x - 24 = 0$ ⓑ ${(y + 5)}^{2} = 12$ ⓒ $14 m^{2} + 3 m = 11$

Answer

ⓐ factor ⓑ square root
ⓒ Quadratic Formula

10.3-137 §10.3 source ↗

Identify the Most Appropriate Method to Use to Solve a Quadratic Equation

In the following exercises, identify the most appropriate method (Factoring, Square Root, or Quadratic Formula) to use to solve each quadratic equation. Do not solve.

ⓐ $6 a^{2} + 14 = 20$ ⓑ ${(x - \frac{1}{4})}^{2} = \frac{5}{16}$ ⓒ $y^{2} - 2 y = 8$

Answer

ⓐ square root ⓑ square root
ⓒ factor

10.3-139 §10.3 source ↗

Identify the Most Appropriate Method to Use to Solve a Quadratic Equation

In the following exercises, identify the most appropriate method (Factoring, Square Root, or Quadratic Formula) to use to solve each quadratic equation. Do not solve.

A flare is fired straight up from a ship at sea. Solve the equation $16 (t^{2} - 13 t + 40) =$ $0$ for $t$ , the number of seconds it will take for the flare to be at an altitude of 640 feet.

Answer

5 seconds, 8 seconds

10.3-141 §10.3 source ↗

Identify the Most Appropriate Method to Use to Solve a Quadratic Equation

In the following exercises, identify the most appropriate method (Factoring, Square Root, or Quadratic Formula) to use to solve each quadratic equation. Do not solve.

Solve the equation $x^{2} + 10 x = 200$
ⓐ by completing the square
ⓑ using the Quadratic Formula
ⓒ Which method do you prefer? Why?

Answer

ⓐ

−20, 10

ⓑ

−20, 10

Be Prepared 10.10 §10.4 source ↗

The sum of two consecutive odd numbers is

−100

. Find the numbers.
If you missed this problem, review Example 3.10.

Example 3.10 in the book ↗

Answer

- 51, - 49

Be Prepared 10.11 §10.4 source ↗

The area of triangular mural is 64 square feet. The base is 16 feet. Find the height.
If you missed this problem, review Example 3.36.

Example 3.36 in the book ↗

Answer

8

Be Prepared 10.12 §10.4 source ↗

Find the length of the hypotenuse of a right triangle with legs 5 inches and 12 inches.
If you missed this problem, review Example 3.39.

Example 3.39 in the book ↗

Answer

13 inches

Try It 10.75 §10.4 source ↗

The product of two consecutive odd integers is 99. Find the integers.

Answer

Two consecutive odd numbers whose product is 99 are 9 and 11, and

−9

and

−11

Try It 10.76 §10.4 source ↗

The product of two consecutive even integers is 168. Find the integers.

Answer

Two consecutive even numbers whose product is 168 are 12 and 14,and

−12

and

−14

Try It 10.77 §10.4 source ↗

Find the dimensions of a triangle whose width is four more than six times its height and has an area of 208 square inches.

Answer

The height of the triangle is 8 inches and the width is 52 inches.

Try It 10.78 §10.4 source ↗

If a triangle that has an area of 110 square feet has a height that is two feet less than twice the width, what are its dimensions?

Answer

The height of the triangle is 20 feet and the width is 11 feet.

Try It 10.79 §10.4 source ↗

The sun casts a shadow from a flag pole. The height of the flag pole is three times the length of its shadow. The distance between the end of the shadow and the top of the flag pole is 20 feet. Find the length of the shadow and the length of the flag pole. Round to the nearest tenth of a foot.

Answer

The length of the shadow is 6.3 feet and the length of the flag pole is 18.9 ft.

Try It 10.80 §10.4 source ↗

The distance between opposite corners of a rectangular field is four more than the width of the field. The length of the field is twice its width. Find the distance between the opposite corners. Round to the nearest tenth.

Answer

The distance to the opposite corner is 3.2.

Try It 10.81 §10.4 source ↗

The length of a 200 square foot rectangular vegetable garden is four feet less than twice the width. Find the length and width of the garden. Round to the nearest tenth of a foot.

Answer

The width of the garden is 11 feet and the length is 18 feet.

Try It 10.82 §10.4 source ↗

A rectangular tablecloth has an area of 80 square feet. The width is 5 feet shorter than the length. What are the length and width of the tablecloth? Round to the nearest tenth of a foot.

Answer

The width of the tablecloth is 6.8 feet and the length is 11.8 feet.

Try It 10.83 §10.4 source ↗

An arrow is shot from the ground into the air at an initial speed of 108 ft/sec. Use the formula

h = −16 t^{2} + v_{0} t

to determine when the arrow will be 180 feet from the ground. Round the nearest tenth of a second.

Answer

The arrow will reach 180 on its way up in 3 seconds, and on the way down in 3.8 seconds.

Try It 10.84 §10.4 source ↗

A man throws a ball into the air with a velocity of 96 ft/sec. Use the formula

h = −16 t^{2} + v_{0} t

to determine when the height of the ball will be 48 feet. Round to the nearest tenth of a second.

Answer

The ball will reach 48 feet on its way up in .6 seconds and on the way down in 5.5 seconds.

10.4-143 §10.4 source ↗

Solve Applications of the Quadratic Formula

In the following exercises, solve by using methods of factoring, the square root principle, or the Quadratic Formula. Round your answers to the nearest tenth.

The product of two consecutive odd numbers is 255. Find the numbers.

Answer

Two consecutive odd numbers whose product is 255 are 15 and 17, and

−15

and

−17

10.4-145 §10.4 source ↗

Solve Applications of the Quadratic Formula

In the following exercises, solve by using methods of factoring, the square root principle, or the Quadratic Formula. Round your answers to the nearest tenth.

The product of two consecutive even numbers is 624. Find the numbers.

Answer

Two consecutive even numbers whose product is 624 are 24 and 26, and

−26

and

−24

10.4-147 §10.4 source ↗

Solve Applications of the Quadratic Formula

In the following exercises, solve by using methods of factoring, the square root principle, or the Quadratic Formula. Round your answers to the nearest tenth.

The product of two consecutive odd numbers is 483. Find the numbers.

Answer

Two consecutive odd numbers whose product is 483 are 21 and 23, and

−21

and

−23

10.4-149 §10.4 source ↗

Solve Applications of the Quadratic Formula

In the following exercises, solve by using methods of factoring, the square root principle, or the Quadratic Formula. Round your answers to the nearest tenth.

A triangle with area 45 square inches has a height that is two less than four times the width. Find the height and width of the triangle.

Answer

The width of the triangle is 5 inches and the height is 18 inches.

10.4-151 §10.4 source ↗

Solve Applications of the Quadratic Formula

In the following exercises, solve by using methods of factoring, the square root principle, or the Quadratic Formula. Round your answers to the nearest tenth.

The hypotenuse of a right triangle is twice the length of one of its legs. The length of the other leg is three feet. Find the lengths of the three sides of the triangle. Round to the nearest tenth.

Answer

The leg of the right triangle is 1.7 feet and the hypotenuse is 3.4 feet.

10.4-153 §10.4 source ↗

Solve Applications of the Quadratic Formula

In the following exercises, solve by using methods of factoring, the square root principle, or the Quadratic Formula. Round your answers to the nearest tenth.

A farmer plans to fence off sections of a rectangular corral. The diagonal distance from one corner of the corral to the opposite corner is five yards longer than the width of the corral. The length of the corral is three times the width. Find the length of the diagonal of the corral. Round to the nearest tenth.

The image shows rectangle with the long sides horizontal. A diagonal line runs from the top left corner of the rectangle to the bottom right corner.

Answer

The length of the diagonal of the fence is 7.3 yards.

10.4-155 §10.4 source ↗

Solve Applications of the Quadratic Formula

In the following exercises, solve by using methods of factoring, the square root principle, or the Quadratic Formula. Round your answers to the nearest tenth.

The length of a rectangular driveway is five feet more than three times the width. The area is 350 square feet. Find the length and width of the driveway.

Answer

The width of the driveway is 10 feet and its length is 35 feet.

10.4-157 §10.4 source ↗

Solve Applications of the Quadratic Formula

In the following exercises, solve by using methods of factoring, the square root principle, or the Quadratic Formula. Round your answers to the nearest tenth.

A firework rocket is shot upward at a rate of 640 ft/sec. Use the projectile formula $h = −16 t^{2} + v_{0} t$ to determine when the height of the firework rocket will be 1200 feet.

Answer

The rocket will reach 1,200 feet on its way up in 2 seconds and on the way down in 38 seconds.

10.4-159 §10.4 source ↗

Solve Applications of the Quadratic Formula

In the following exercises, solve by using methods of factoring, the square root principle, or the Quadratic Formula. Round your answers to the nearest tenth.

A bullet is fired straight up from a BB gun with initial velocity 1120 feet per second at an initial height of 8 feet. Use the formula $h =$ $−16 t^{2} +$ $v_{0} t +$ $8$ to determine how many seconds it will take for the bullet to hit the ground. (That is, when will $h = 0$ ?)

Answer

70 seconds

10.4-161 §10.4 source ↗

Solve Applications of the Quadratic Formula

In the following exercises, solve by using methods of factoring, the square root principle, or the Quadratic Formula. Round your answers to the nearest tenth.

Make up a problem involving the product of two consecutive odd integers. Start by choosing two consecutive odd integers. ⓐ What are your integers? ⓑ What is the product of your integers? ⓒ Solve the equation $n (n + 2) = p$ , where $p$ is the product you found in part (b). ⓓ Did you get the numbers you started with?

Answer

ⓐ answers will vary
ⓑ answers will vary ⓒ answers will vary ⓓ answers will vary

Be Prepared 10.13 §10.5 source ↗

Graph the equation

y = 3 x - 5

by plotting points.
If you missed this problem, review Example 4.11.

Example 4.11 in the book ↗

Answer

A graph shows a straight line with a positive slope in a Cartesian coordinate system. The line passes through approximately (0, -5), (1, -2), (2, 1), and (3, 4).

Be Prepared 10.14 §10.5 source ↗

Evaluate

2 x^{2} + 4 x - 1

when

x = −3

.
If you missed this problem, review Example 1.57.

Example 1.57 in the book ↗

Answer

5

Be Prepared 10.15 §10.5 source ↗

Evaluate

- \frac{b}{2 a}

when

a = \frac{1}{3}

and

b = \frac{5}{6}

.
If you missed this problem, review Example 1.89.

Example 1.89 in the book ↗

Answer

- \frac{5}{4}

Try It 10.85 §10.5 source ↗

Graph

y = − x^{2}

Answer

Try It 10.86 §10.5 source ↗

Graph

y = x^{2} + 1

Answer

This figure shows an upward-opening u shaped curve graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The lowest point on the curve is at the point (0, 1). Other points on the curve are located at (-2, 5), (-1, 2), (1, 2) and (2, 5).

Try It 10.87 §10.5 source ↗

Determine whether each parabola opens upward or downward:

ⓐ $y = 2 x^{2} + 5 x - 2$ ⓑ $y = −3 x^{2} - 4 x + 7$

Answer

ⓐ up ⓑ down

Try It 10.88 §10.5 source ↗

Determine whether each parabola opens upward or downward:

ⓐ $y = −2 x^{2} - 2 x - 3$ ⓑ $y = 5 x^{2} - 2 x - 1$

Answer

ⓐ down ⓑ up

Try It 10.89 §10.5 source ↗

For the parabola

y = 2 x^{2} - 8 x + 1

find: ⓐ the axis of symmetry and ⓑ the vertex.

Answer

ⓐ

x = 2

ⓑ

(2, −7)

Try It 10.90 §10.5 source ↗

For the parabola

y = 2 x^{2} - 4 x - 3

find: ⓐ the axis of symmetry and ⓑ the vertex.

Answer

ⓐ

x = 1

ⓑ

(1, −5)

Try It 10.91 §10.5 source ↗

Find the intercepts of the parabola

y = x^{2} + 2 x - 8 .

Answer

y : (0, −8);

x : (−4, 0),

(2, 0)

Try It 10.92 §10.5 source ↗

Find the intercepts of the parabola

y = x^{2} - 4 x - 12 .

Answer

y : (0, −12);

x : (6, 0),

(−2, 0)

Try It 10.93 §10.5 source ↗

Find the intercepts of the parabola

y = 3 x^{2} + 4 x + 4 .

Answer

y : (0, 4);

x : none

Try It 10.94 §10.5 source ↗

Find the intercepts of the parabola

y = x^{2} - 4 x - 5 .

Answer

y : (0, −5);

x : (5, 0) (−1, 0)

Try It 10.95 §10.5 source ↗

Find the intercepts of the parabola

y =

− x^{2} -

12 x -

36 .

Answer

y : (0, −36);

x : (−6, 0)

Try It 10.96 §10.5 source ↗

Find the intercepts of the parabola

y =

9 x^{2} +

12 x +

4 .

Answer

y : (0, 4);

x : (- \frac{2}{3}, 0)

Try It 10.97 §10.5 source ↗

Graph the parabola

y = x^{2} + 2 x - 8 .

Answer

$y : (0, −8)$ ; $x : (2, 0),$ $(−4, 0)$ ;
axis: $x = −1$ ; vertex: $(−1, −9)$ ;

The graph shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The vertex is at the point (-1, -9). Three points are plotted on the curve at (0, -8), (2, 0) and (-4, 0). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals -1.

Try It 10.98 §10.5 source ↗

Graph the parabola

y = x^{2} - 8 x + 12 .

Answer

$y : (0, 12);$ $x : (2, 0),$ $(6, 0);$
axis: $x =$ $4;$ $vertex: (4, −4)$ ;

Try It 10.99 §10.5 source ↗

Graph the parabola

y =

−3 x^{2} +

12 x -

12 .

Answer

$y : (0, −12);$ $x : (2, 0);$
axis: $x =$ $2;$ $vertex: (2, 0)$ ;

The graph shows an downward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -1 to 10. The vertex is at the point (2, 0). One other point is plotted on the curve at (0, -12). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals 2.

Try It 10.100 §10.5 source ↗

Graph the parabola

y =

25 x^{2} +

10 x +

1 .

Answer

$y : (0, 1);$ $x : (- \frac{1}{5}, 0);$
axis: $x =$ $-$ $\frac{1}{5};$ $vertex: (- \frac{1}{5}, 0)$ ;

The graph shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -5 to 5. The y-axis of the plane runs from -5 to 10. The vertex is at the point (-1 fifth, 0). One other point is plotted on the curve at (0, 1). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals -1 fifth.

Try It 10.101 §10.5 source ↗

Graph the parabola

y = 2 x^{2} - 6 x + 5 .

Answer

$y : (0, 5);$ $x : none;$
axis: $x =$ $\frac{3}{2};$ $vertex: (\frac{3}{2}, \frac{1}{2})$ ;

Try It 10.102 §10.5 source ↗

Graph the parabola

y = −2 x^{2} - 1 .

Answer

$y : (0, −1);$ $x : none;$
axis: $x =$ $0;$ $vertex: (0, −1)$ ;

Try It 10.103 §10.5 source ↗

Graph the parabola

y =

5 x^{2} +

10 x +

3 .

Answer

$y : (0, 3);$ $x : (−1.6, 0),$ $(−0.4, 0);$
axis: $x =$ $−1;$ $vertex: (−1, −2)$ ;

Try It 10.104 §10.5 source ↗

Graph the parabola

y =

−3 x^{2} -

6 x +

5 .

Answer

$y : (0, 5);$ $x : (0.6, 0),$ $(−2.6, 0);$
axis: $x =$ $−1;$ $vertex: (−1, 8)$ ;

Try It 10.105 §10.5 source ↗

Find the maximum or minimum value of the quadratic equation

y = x^{2} - 8 x + 12

Answer

The minimum value is

−4

when

x = 4

Try It 10.106 §10.5 source ↗

Find the maximum or minimum value of the quadratic equation

y =

−4 x^{2} +

16 x -

11

Answer

The maximum value is 5 when

x = 2

Try It 10.107 §10.5 source ↗

The quadratic equation

h =

−16 t^{2} +

128 t +

32

is used to find the height of a stone thrown upward from a height of 32 feet at a rate of 128 ft/sec. How long will it take for the stone to reach its maximum height? What is the maximum height? Round answers to the nearest tenth.

Answer

It will take 4 seconds to reach the maximum height of 288 feet.

Try It 10.108 §10.5 source ↗

A toy rocket shot upward from the ground at a rate of 208 ft/sec has the quadratic equation of

h =

−16 t^{2} +

208 t

. When will the rocket reach its maximum height? What will be the maximum height? Round answers to the nearest tenth.

Answer

It will take 6.5 seconds to reach the maximum height of 676 feet.

10.5-163 §10.5 source ↗

Recognize the Graph of a Quadratic Equation in Two Variables

In the following exercises, graph:

$y = x^{2} + 3$

Answer

This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The parabola has a vertex at (0, 3) and goes through the point (1, 4).

10.5-165 §10.5 source ↗

In the following exercises, determine if the parabola opens up or down.

$y = −2 x^{2} - 6 x - 7$

Answer

down

10.5-167 §10.5 source ↗

In the following exercises, determine if the parabola opens up or down.

$y = 4 x^{2} + x - 4$

Answer

10.5-169 §10.5 source ↗

Find the Axis of Symmetry and Vertex of a Parabola

In the following exercises, find ⓐ the axis of symmetry and ⓑ the vertex.

$y = x^{2} + 8 x - 1$

Answer

ⓐ

x = −4

ⓑ

(−4, −17)

10.5-171 §10.5 source ↗

Find the Axis of Symmetry and Vertex of a Parabola

In the following exercises, find ⓐ the axis of symmetry and ⓑ the vertex.

$y = − x^{2} + 2 x + 5$

Answer

ⓐ

x = 1

ⓑ

(1, 6)

10.5-173 §10.5 source ↗

Find the Intercepts of a Parabola

In the following exercises, find the x- and y-intercepts.

$y = x^{2} + 7 x + 6$

Answer

y : (0, 6);

x : (−1, 0),

(−6, 0)

10.5-175 §10.5 source ↗

Find the Intercepts of a Parabola

In the following exercises, find the x- and y-intercepts.

$y = − x^{2} + 8 x - 19$

Answer

y : (0, - 19);

x : none

10.5-177 §10.5 source ↗

Find the Intercepts of a Parabola

In the following exercises, find the x- and y-intercepts.

$y =$ $4 x^{2} -$ $20 x +$ $25$

Answer

y : (0, 25);

x : (\frac{5}{2}, 0)

10.5-179 §10.5 source ↗

Graph Quadratic Equations in Two Variables

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.

$y = x^{2} + 6 x + 5$

Answer

$y : (0, 5);$ $x : (−1, 0),$ $(−5, 0);$
axis: $x =$ $−3;$ $vertex : (−3, −4)$

10.5-181 §10.5 source ↗

Graph Quadratic Equations in Two Variables

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.

$y = x^{2} + 4 x + 3$

Answer

$y : (0, 3);$ $x : (−1, 0),$ $(−3, 0);$
axis: $x =$ $−2;$ $vertex: (−2, −1)$

10.5-183 §10.5 source ↗

Graph Quadratic Equations in Two Variables

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.

$y = 9 x^{2} + 12 x + 4$

Answer

$y : (0, 4) x : (- \frac{2}{3}, 0);$
axis: $x =$ $-$ $\frac{2}{3};$ $vertex: (- \frac{2}{3}, 0)$

This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -5 to 5. The y-axis of the plane runs from -5 to 5. The parabola has points plotted at the vertex (-2 thirds, 0) and the intercept (0, 4). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals -2 thirds.

10.5-185 §10.5 source ↗

Graph Quadratic Equations in Two Variables

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.

$y = − x^{2} + 2 x - 7$

Answer

$y : (0, −7);$ $x : none;$
axis: $x =$ $1;$ $vertex : (1, −6)$

This figure shows a downward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -15 to 5. The parabola has points plotted at the vertex (1, -6) and the intercept (0, -7). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals 1.

10.5-187 §10.5 source ↗

Graph Quadratic Equations in Two Variables

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.

$y = 2 x^{2} - 4 x + 1$

Answer

$y : (0, 1);$ $x : (1.7, 0),$ $(0.3, 0);$
axis: $x =$ $1;$ $vertex : (1, −1)$

10.5-189 §10.5 source ↗

Graph Quadratic Equations in Two Variables

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.

$y = 2 x^{2} - 4 x + 2$

Answer

$y : (0, 2) x : (1, 0);$
axis: $x =$ $1;$ $vertex: (1, 0)$

10.5-191 §10.5 source ↗

Graph Quadratic Equations in Two Variables

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.

$y = − x^{2} - 4 x + 2$

Answer

$y : (0, 2) x : (−4.4, 0),$ $(0.4, 0);$
axis: $x =$ $−2;$ $vertex: (−2, 6)$

10.5-193 §10.5 source ↗

Graph Quadratic Equations in Two Variables

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.

$y = 5 x^{2} - 10 x + 8$

Answer

$y : (0, 8);$ $x : none;$
axis: $x =$ $1;$ $vertex : (1, 3)$

10.5-195 §10.5 source ↗

Graph Quadratic Equations in Two Variables

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.

$y =$ $3 x^{2} +$ $18 x +$ $20$

Answer

$y : (0, 20) x : (−4.5, 0),$ $(−1.5, 0);$
axis: $x =$ $−3;$ $vertex: (−3, −7)$

10.5-197 §10.5 source ↗

Solve Maximum and Minimum Applications

In the following exercises, find the maximum or minimum value.

$y = 2 x^{2} + x - 1$

Answer

The minimum value is

- \frac{9}{8}

when

x = - \frac{1}{4}

10.5-199 §10.5 source ↗

Solve Maximum and Minimum Applications

In the following exercises, find the maximum or minimum value.

$y = x^{2} - 6 x + 15$

Answer

The minimum value is 6 when

x = 3

10.5-201 §10.5 source ↗

Solve Maximum and Minimum Applications

In the following exercises, find the maximum or minimum value.

$y = −9 x^{2} + 16$

Answer

The maximum value is 16 when

x = 0

10.5-203 §10.5 source ↗

In the following exercises, solve. Round answers to the nearest tenth.

An arrow is shot vertically upward from a platform 45 feet high at a rate of 168 ft/sec. Use the quadratic equation $h =$ $−16 t^{2} +$ $168 t +$ $45$ to find how long it will take the arrow to reach its maximum height, and then find the maximum height.

Answer

In 5.3 sec the arrow will reach maximum height of 486 ft.

10.5-205 §10.5 source ↗

In the following exercises, solve. Round answers to the nearest tenth.

A computer store owner estimates that by charging $x$ dollars each for a certain computer, he can sell $40 - x$ computers each week. The quadratic equation $R = − x^{2} + 40 x$ is used to find the revenue, $R$ , received when the selling price of a computer is $x$ . Find the selling price that will give him the maximum revenue, and then find the amount of the maximum revenue.

Answer

Charging $20 for each computer will give the maximum revenue of $400.

10.5-207 §10.5 source ↗

In the following exercises, solve. Round answers to the nearest tenth.

A rancher is going to fence three sides of a corral next to a river. He needs to maximize the corral area using 240 feet of fencing. The quadratic equation $A = x (240 - 2 x)$ gives the area of the corral, $A$ , for the length, $x,$ of the corral along the river. Find the length of the corral along the river that will give the maximum area, and then find the maximum area of the corral.

Answer

The length of the side along the river of the corral is 60 feet and the maximum area is 7,200 sq ft.

10.5-209 §10.5 source ↗

In the following exercises, solve. Round answers to the nearest tenth.

In the previous set of exercises, you worked with the quadratic equation $R = − x^{2} + 40 x$ that modeled the revenue received from selling computers at a price of $x$ dollars. You found the selling price that would give the maximum revenue and calculated the maximum revenue. Now you will look at more characteristics of this model.
ⓐ Graph the equation $R = − x^{2} + 40 x$ . ⓑ Find the values of the x-intercepts.

Answer

ⓐ
This figure shows a downward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 60. The y-axis of the plane runs from -50 to 500. The parabola has a vertex at (20, 400) and also goes through the points (0, 0) and (40, 0).

ⓑ $(0, 0),$ $(40, 0)$

10.5-211 §10.5 source ↗

In the following exercises, solve. Round answers to the nearest tenth.

For the revenue model in Exercise 10.205 and Exercise 10.209, explain what the x-intercepts mean to the computer store owner.

Answer

Answers will vary.

10.R-213 §10.R source ↗

In the following exercises, solve using the Square Root Property.

$x^{2} = 100$

Answer

x = \pm 10

10.R-215 §10.R source ↗

In the following exercises, solve using the Square Root Property.

$m^{2} - 40 = 0$

Answer

m = \pm 2 \sqrt{10}

10.R-217 §10.R source ↗

In the following exercises, solve using the Square Root Property.

$4 a^{2} = 100$

Answer

a = \pm 5

10.R-219 §10.R source ↗

In the following exercises, solve using the Square Root Property.

$r^{2} + 32 = 0$

Answer

no solution

10.R-221 §10.R source ↗

In the following exercises, solve using the Square Root Property.

$\frac{4}{3} v^{2} + 4 = 28$

Answer

v = \pm 3 \sqrt{2}

10.R-223 §10.R source ↗

In the following exercises, solve using the Square Root Property.

$5 c^{2} + 3 = 19$

Answer

c = \pm \frac{4 \sqrt{5}}{5}

10.R-225 §10.R source ↗

In the following exercises, solve using the Square Root Property.

${(p - 5)}^{2} + 3 = 19$

Answer

p = 1, 9

10.R-227 §10.R source ↗

In the following exercises, solve using the Square Root Property.

${(u + 1)}^{2} = 45$

Answer

u = −1 \pm 3 \sqrt{5}

10.R-229 §10.R source ↗

In the following exercises, solve using the Square Root Property.

${(x - \frac{1}{4})}^{2} = \frac{3}{16}$

Answer

x = \frac{1}{4} \pm \frac{\sqrt{3}}{4}

10.R-231 §10.R source ↗

In the following exercises, solve using the Square Root Property.

${(m - 7)}^{2} + 6 = 30$

Answer

m = 7 \pm 2 \sqrt{6}

10.R-233 §10.R source ↗

In the following exercises, solve using the Square Root Property.

${(5 c + 3)}^{2} = −20$

Answer

no solution

10.R-235 §10.R source ↗

In the following exercises, solve using the Square Root Property.

$m^{2} - 6 m + 9 = 48$

Answer

m = 3 \pm 4 \sqrt{3}

10.R-237 §10.R source ↗

In the following exercises, solve using the Square Root Property.

$64 a^{2} +$ $48 a +$ $9 =$ $81$

Answer

a = - \frac{3}{2}, \frac{3}{4}

10.R-239 §10.R source ↗

In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.

$x^{2} + 22 x$

Answer

{(x + 11)}^{2}

10.R-241 §10.R source ↗

In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.

$m^{2} - 8 m$

Answer

{(m - 4)}^{2}

10.R-243 §10.R source ↗

In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.

$a^{2} - 3 a$

Answer

{(a - \frac{3}{2})}^{2}

10.R-245 §10.R source ↗

In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.

$p^{2} + \frac{4}{5} p$

Answer

{(p + \frac{2}{5})}^{2}

10.R-247 §10.R source ↗

In the following exercises, solve by completing the square.

$c^{2} + 20 c = 21$

Answer

c = 1, −21

10.R-249 §10.R source ↗

In the following exercises, solve by completing the square.

$x^{2} - 4 x = 32$

Answer

x = −4, 8

10.R-251 §10.R source ↗

In the following exercises, solve by completing the square.

$r^{2} + 6 r = −100$

Answer

no solution

10.R-253 §10.R source ↗

In the following exercises, solve by completing the square.

$v^{2} - 14 v = −31$

Answer

v = 7 \pm 3 \sqrt{2}

10.R-255 §10.R source ↗

In the following exercises, solve by completing the square.

$m^{2} +$ $10 m -$ $4 =$ $−13$

Answer

m = −9, −1

10.R-257 §10.R source ↗

In the following exercises, solve by completing the square.

$a^{2} = 3 a + 8$

Answer

a = \frac{3}{2} \pm \frac{\sqrt{41}}{2}

10.R-259 §10.R source ↗

In the following exercises, solve by completing the square.

$(u + 8) (u + 4) =$ $14$

Answer

u = −6 \pm 3 \sqrt{2}

10.R-261 §10.R source ↗

In the following exercises, solve by completing the square.

$3 p^{2} -$ $18 p +$ $15 =$ $15$

Answer

p = 0, 6

10.R-263 §10.R source ↗

In the following exercises, solve by completing the square.

$4 y^{2} - 6 y = 4$

Answer

y = - \frac{1}{2}, 2

10.R-265 §10.R source ↗

In the following exercises, solve by completing the square.

$3 c^{2} + 2 c = 9$

Answer

c = - \frac{1}{3} \pm \frac{2 \sqrt{7}}{3}

10.R-267 §10.R source ↗

In the following exercises, solve by using the Quadratic Formula.

$4 x^{2} - 5 x + 1 = 0$

Answer

x = \frac{1}{4}, 1

10.R-269 §10.R source ↗

In the following exercises, solve by using the Quadratic Formula.

$r^{2} - r - 42 = 0$

Answer

r = −6, 7

10.R-271 §10.R source ↗

In the following exercises, solve by using the Quadratic Formula.

$4 v^{2} + v - 5 = 0$

Answer

v = - \frac{5}{4}, 1

10.R-273 §10.R source ↗

In the following exercises, solve by using the Quadratic Formula.

$3 m^{2} + 8 m + 2 = 0$

Answer

m = \frac{−4 \pm \sqrt{10}}{3}

10.R-275 §10.R source ↗

In the following exercises, solve by using the Quadratic Formula.

$6 a^{2} - 5 a + 2 = 0$

Answer

no real solution

10.R-277 §10.R source ↗

In the following exercises, solve by using the Quadratic Formula.

$u (u - 10) + 3 = 0$

Answer

u = 5 \pm \sqrt{22}

10.R-279 §10.R source ↗

In the following exercises, solve by using the Quadratic Formula.

$\frac{1}{8} p^{2} -$ $\frac{1}{5} p =$ $-$ $\frac{1}{20}$

Answer

p = \frac{4 \pm \sqrt{6}}{5}

10.R-281 §10.R source ↗

In the following exercises, solve by using the Quadratic Formula.

$4 c^{2} + 4 c + 1 = 0$

Answer

c = - \frac{1}{2}

10.R-283 §10.R source ↗

In the following exercises, determine the number of solutions to each quadratic equation.

ⓐ $9 x^{2} - 6 x + 1 = 0$

ⓑ $3 y^{2} - 8 y + 1 = 0$

ⓓ $5 n^{2} - n + 1 = 0$

Answer

10.R-285 §10.R source ↗

In the following exercises, identify the most appropriate method (Factoring, Square Root, or Quadratic Formula) to use to solve each quadratic equation.

ⓐ $16 r^{2} - 8 r + 1 = 0$

ⓑ $5 t^{2} - 8 t + 3 = 9$

Answer

10.R-287 §10.R source ↗

In the following exercises, solve by using methods of factoring, the square root principle, or the quadratic formula.

Find two consecutive odd numbers whose product is 323.

Answer

Two consecutive odd numbers whose product is 323 are 17 and 19, and

−17

and

−19 .

10.R-289 §10.R source ↗

In the following exercises, solve by using methods of factoring, the square root principle, or the quadratic formula.

A triangular banner has an area of 351 square centimeters. The length of the base is two centimeters longer than four times the height. Find the height and length of the base.

Answer

The height of the banner is 13 cm and the length of the side is 54 cm.

10.R-291 §10.R source ↗

In the following exercises, solve by using methods of factoring, the square root principle, or the quadratic formula.

A tile mosaic in the shape of a right triangle is used as the corner of a rectangular pathway. The hypotenuse of the mosaic is 5 feet. One side of the mosaic is twice as long as the other side. What are the lengths of the sides? Round to the nearest tenth.

Answer

The lengths of the sides of the mosaic are 2.2 and 4.4 feet.

10.R-293 §10.R source ↗

In the following exercises, solve by using methods of factoring, the square root principle, or the quadratic formula.

The front walk from the street to Pam’s house has an area of 250 square feet. Its length is two less than four times its width. Find the length and width of the sidewalk. Round to the nearest tenth.

Answer

The width of the front walk is 8.2 feet and its length is 30.6 feet.

10.R-295 §10.R source ↗

In the following exercises, solve by using methods of factoring, the square root principle, or the quadratic formula.

A ball is thrown vertically in the air with a velocity of 160 ft/sec. Use the formula $h = −16 t^{2} + v_{0} t$ to determine when the ball will be 384 feet from the ground. Round to the nearest tenth.

Answer

The ball will reach 384 feet on its way up in 4 seconds and on the way down in 6 seconds.

10.R-297 §10.R source ↗

In the following exercises, graph by plotting point.

Graph $y = x^{2} - 2$

Answer

10.R-299 §10.R source ↗

In the following exercises, determine if the following parabolas open up or down.

$y = −3 x^{2} + 3 x - 1$

Answer

down

10.R-301 §10.R source ↗

In the following exercises, determine if the following parabolas open up or down.

$y = x^{2} + 8 x - 1$

Answer

10.R-303 §10.R source ↗

In the following exercises, find ⓐ the axis of symmetry and ⓑ the vertex.

$y = − x^{2} + 6 x + 8$

Answer

ⓐ

x = 3

ⓑ

(3, 17)

10.R-305 §10.R source ↗

In the following exercises, find the x- and y-intercepts.

$y = x^{2} - 4 x - 5$

Answer

y : (0, 5);

x : (5, 0),

(−1, 0)

10.R-307 §10.R source ↗

In the following exercises, find the x- and y-intercepts.

$y = x^{2} - 4 x + 10$

Answer

y : (0, 10);

x : none

10.R-309 §10.R source ↗

In the following exercises, find the x- and y-intercepts.

$y = 16 x^{2} - 8 x + 1$

Answer

y : (0, 1);

x : (\frac{1}{4}, 0)

10.R-311 §10.R source ↗

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.

$y = x^{2} + 8 x + 15$

Answer

$y : (0, 15);$ $x : (−3, 0),$ $(−5, 0);$
axis: $x =$ $−4;$ $vertex : (−4, −1)$

10.R-313 §10.R source ↗

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.

$y = − x^{2} + 8 x - 16$

Answer

$y : (0, −16);$ $x : (4, 0);$
axis: $x =$ $4;$ $vertex : (4, 0)$

This figure shows a downward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -15 to 12. The y-axis of the plane runs from -20 to 2. The parabola has points plotted at the vertex (4, 0) and the intercept (0, -16). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals 4.

10.R-315 §10.R source ↗

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.

$y = x^{2} + 6 x + 13$

Answer

$y : (0, 13);$ $x : none;$
axis: $x =$ $−3;$ $vertex : (−3, 4)$

10.R-317 §10.R source ↗

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.

$y =$ $−4 x^{2} +$ $16 x -$ $11$

Answer

$y : (0, −11) x : (3.1, 0),$ $(0.9, 0);$
axis: $x =$ $2;$ $vertex: (2, 5)$

10.R-319 §10.R source ↗

In the following exercises, find the minimum or maximum value.

$y = 7 x^{2} + 14 x + 6$

Answer

The minimum value is

−1

when

x = −1

10.R-321 §10.R source ↗

In the following exercises, solve. Rounding answers to the nearest tenth.

A ball is thrown upward from the ground with an initial velocity of 112 ft/sec. Use the quadratic equation $h =$ $−16 t^{2} +$ $112 t$ to find how long it will take the ball to reach maximum height, and then find the maximum height.

Answer

In 3.5 seconds the ball is at its maximum height of 196 feet.

10.T-323 §10.T source ↗

Use the Square Root Property to solve the quadratic equation:

3 {(w + 5)}^{2} = 27

Answer

w = −2, −8

10.T-325 §10.T source ↗

Use the Quadratic Formula to solve the quadratic equation:

2 m^{2} - 5 m + 3 = 0

Answer

m = 1, \frac{3}{2}

10.T-327 §10.T source ↗

Solve the following quadratic equations. Use any method.

$3 n^{2} + 8 n + 3 = 0$

Answer

n = \frac{−4 \pm \sqrt{7}}{3}

10.T-329 §10.T source ↗

Solve the following quadratic equations. Use any method.

$x (x + 3) + 12 = 0$

Answer

no real solution

10.T-331 §10.T source ↗

Use the discriminant to determine the number of solutions of each quadratic equation.

$6 p^{2} - 13 p + 7 = 0$

Answer

10.T-333 §10.T source ↗

Solve by factoring, the Square Root Property, or the Quadratic Formula.

Find two consecutive even numbers whose product is 360.

Answer

Two consecutive even number are

−20

and

−18

and 18 and 20.

10.T-335 §10.T source ↗

For each parabola, find ⓐ which ways it opens, ⓑ the axis of symmetry, ⓒ the vertex, ⓓ the x- and y-intercepts, and ⓔ the maximum or minimum value.

$y = 3 x^{2} + 6 x + 8$

Answer

ⓐ up ⓑ

x = −1

ⓒ

(−1, 5)

ⓓ

y : (0, 8);

x : none

ⓔ minimum value of 5 when

x = −1

10.T-337 §10.T source ↗

For each parabola, find ⓐ which ways it opens, ⓑ the axis of symmetry, ⓒ the vertex, ⓓ the x- and y-intercepts, and ⓔ the maximum or minimum value.

$y = x^{2} + 10 x + 24$

Answer

ⓐ up ⓑ

x = −5

ⓒ

(−5, −1)

ⓓ

y;

(0, 24);

x : (−6, 0),

(−4, 0)

ⓔ minimum value of

−1

when

x = −5

10.T-339 §10.T source ↗

For each parabola, find ⓐ which ways it opens, ⓑ the axis of symmetry, ⓒ the vertex, ⓓ the x- and y-intercepts, and ⓔ the maximum or minimum value.

$y = − x^{2} - 8 x + 16$

Answer

ⓐ down ⓑ

x = −4

ⓒ

(−4, 32)

ⓓ

y;

(0, 16);

x : (−9.7, 0),

(1.7, 0)

ⓔ maximum value of

32

when

x = −4

10.T-341 §10.T source ↗

Graph the following parabolas by using intercepts, the vertex, and the axis of symmetry.

$y =$ $16 x^{2} +$ $24 x +$ $9$

Answer

$y : (0, 9);$ $x : (- \frac{3}{4}, 0);$
axis: $x =$ $-$ $\frac{3}{4};$ $vertex : (- \frac{3}{4}, 0)$

End of the book.

Problems and answers are adapted from Elementary Algebra 2e by Lynn Marecek and MaryAnne Anthony-Smith, OpenStax, and are used under the CC BY-NC-SA 4.0 licence. Access for free at https://openstax.org/books/elementary-algebra-2e/pages/1-introduction. Illustrations: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license. This adaptation is released under the same licence, is non-commercial, and is neither affiliated with nor endorsed by OpenStax or Rice University.