Deck 8: Quadratic Equations and Functions

Question 1

Use the square root property to solve the equation.
$( x + 2 ) ^ { 2 } = 24$

A) $\{ 2 \sqrt { 6 } - 2,2 \sqrt { 6 } + 2 \}$
B) $\{ - 2 \sqrt { 6 } , 2 \sqrt { 6 } \}$
C) $\{ - 2 - 2 \sqrt { 6 } , - 2 + 2 \sqrt { 6 } \}$
D) $\{ - 2 - 2 \sqrt { 12 } , - 2 + 2 \sqrt { 12 } \}$

Answer 1

C

Question 2

Use the square root property to solve the equation.
$( x - 2 ) ^ { 2 } = 16$

A) $\{ 4 , - 4 \}$
B) $\{ 18 \}$
C) $\{ - 2 , - 6 \}$
D) $\{ 6 , - 2 \}$

Answer 2

D

Question 3

$x ^ { 2 } = 64$

A) $\{ - 8,8 \}$
B) $\{ 32 \}$
C) $\{ - 9,9 \}$
D) $\{ 8 \}$

Answer 3

A

Question 4

Use the square root property to solve the equation.
$( x + 2 ) ^ { 2 } = 17$

A) $\{ 15 \}$
B) $\{ 2 - \sqrt { 17 } , 2 + \sqrt { 17 } \}$
C) $\{ - 2 - \sqrt { 17 } , - 2 + \sqrt { 17 } \}$
D) $\{ - \sqrt { 17 } , \sqrt { 17 } \}$

Question 5

Use the square root property to solve the equation.
$( 3 x + 4 ) ^ { 2 } + 5 = 0$

A) $\left\{ \frac { - 4 + i \sqrt { 5 } } { 3 } , \frac { - 4 - i \sqrt { 5 } } { 3 } \right\}$
B) $\left\{ \frac { \sqrt { 5 } + 4 } { 3 } , \frac { \sqrt { 5 } - 4 } { 3 } \right\}$
C) $\left\{ \frac { - 4 + \sqrt { 5 } } { 3 } , \frac { - 4 - \sqrt { 5 } } { 3 } \right\}$
D) $\left\{ - \frac { 9 } { 3 } , \frac { 1 } { 3 } \right\}$

Question 6

Use the square root property to solve the equation.
$( x + 1 ) ^ { 2 } = - 63$

A) $\{ - 1 - 3 \sqrt { 7 } , - 1 + 3 \sqrt { 7 } \}$
B) $\{ - 1 - 3 i \sqrt { 7 } , - 1 + 3 i \sqrt { 7 } \}$
C) $\{ 3 i \sqrt { 7 } - 1,3 i \sqrt { 7 } + 1 \}$
D) $\{ 1 - 3 \mathrm { i } \sqrt { 7 } , 1 + 3 \mathrm { i } \sqrt { 7 } \}$

Question 7

Use the square root property to solve the equation.
$x ^ { 2 } = 22$

A) $\{ 11 \}$
B) $\{ - \sqrt { 22 } , \sqrt { 22 } \}$
C) $\{ \sqrt { 22 } \}$
D) $\{ 484 \}$

Question 8

Use the square root property to solve the equation.
$x ^ { 2 } + 81 = 0$

A) $\{ 9 \}$
B) $\{ - 9,9 \}$
C) $\{ 6561 \}$
D) $\{ - 9 i , 9 i \}$

Question 9

Use the square root property to solve the equation.
$( 4 x - 1 ) ^ { 2 } = \frac { 4 } { 16 }$

A) $\left\{ \frac { 3 } { 8 } , \frac { 1 } { 8 } \right\}$
B) $\left\{ - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right\}$
C) $\{ 3 , - 1 \}$
D) $\left\{ - \frac { 1 } { 8 } , \frac { 1 } { 8 } \right\}$

Question 10

Use the square root property to solve the equation.
$4 x ^ { 2 } = 60$

A) $\{ 16 \}$
B) $\{ - 15,15 \}$
C) $\{ 30 \}$
D) $\{ - \sqrt { 15 } , \sqrt { 15 } \}$

Question 11

Use the square root property to solve the equation.
$4 x ^ { 2 } - 60 = 0$

A) $\{ 30 \}$
B) $\{ 16 \}$
C) $\{ - 15,15 \}$
D) $\{ - \sqrt { 15 } , \sqrt { 15 } \}$

Question 12

Use the square root property to solve the equation.
$x ^ { 2 } - 19 = 0$

A) $\{ - \sqrt { 19 } , \sqrt { 19 } \}$
B) $\left\{ \frac { 19 } { 2 } \right\}$
C) $\{ \sqrt { 19 } \}$
D) $\{ 361 \}$

Question 13

Use the square root property to solve the equation.
$( 2 x + 2 ) ^ { 2 } = 16$

A) $\{ 0,1 \}$
B) $\{ 1 , - 3 \}$
C) $\{ 1,3 \}$
D) $\{ 9 , - 9 \}$

Question 14

Use the square root property to solve the equation.
$( x + 6 ) ^ { 2 } = - 121$

A) $\{ - 17,5 \}$
B) $\{ - 6 - 11 i , - 6 + 11 i \}$
C) $\{ - 5,17 \}$
D) $\{ 6 - 11 i , 6 + 11 i \}$

Question 15

Use the square root property to solve the equation.
$( 11 - 9 x ) ^ { 2 } = 35$

A) $\left\{ \frac { \sqrt { 35 - 11 } } { 9 } , \frac { \sqrt { 35 + 11 } } { 9 } \right\}$
B) $\left\{ \frac { 9 - \sqrt { 35 } } { 11 } , \frac { 9 + \sqrt { 35 } } { 11 } \right\}$
C) $\left\{ \frac { 46 } { 9 } , - \frac { 8 } { 3 } \right\}$
D) $\left\{ \frac { 11 - \sqrt { 35 } } { 9 } , \frac { 11 + \sqrt { 35 } } { 9 } \right\}$

Question 16

Use the square root property to solve the equation.
$( 2 x - 1 ) ^ { 2 } = 25$

A) $\{ 4 , - 6 \}$
B) $\{ 2 , - 3 \}$
C) $\{ 3 , - 2 \}$
D) $\{ 6 , - 4 \}$

Question 17

Use the square root property to solve the equation.
$( 4 x + 3 ) ^ { 2 } = 6$

A) $\left\{ - \frac { 9 } { 4 } , \frac { 3 } { 4 } \right\}$
B) $\left\{ \frac { - 3 - \sqrt { 6 } } { 4 } , \frac { - 3 + \sqrt { 6 } } { 4 } \right\}$
C) $\left\{ \frac { \sqrt { 6 } - 3 } { 4 } , \frac { \sqrt { 6 } + 3 } { 4 } \right\}$
D) $\left\{ \frac { 3 - \sqrt { 6 } } { 4 } , \frac { 3 + \sqrt { 6 } } { 4 } \right\}$

Question 18

Use the square root property to solve the equation.
$x ^ { 2 } = 120$

A) $\{ 60 \}$
B) $\{ 12 \}$
C) $\{ - 2 \sqrt { 30 } , 2 \sqrt { 30 } \}$
D) $\{ 2 \sqrt { 30 } \}$

Question 19

Use the square root property to solve the equation.
$11 x ^ { 2 } = 144$

A) $\left\{ \frac { 12 \sqrt { 11 } } { 11 } \right\}$
B) $\left\{ - \frac { \sqrt { 1584 } } { 11 } , \frac { \sqrt { 1584 } } { 11 } \right\}$
C) $\left\{ - \frac { 12 } { 11 } , \frac { 12 } { 11 } \right\}$
D) $\left\{ - \frac { 12 \sqrt { 11 } } { 11 } , \frac { 12 \sqrt { 11 } } { 11 } \right\}$

Question 20

Use the square root property to solve the equation.
$2 x ^ { 2 } + 14 = 0$

A) $\{ - \mathrm { i } \sqrt { 7 } , \mathrm { i } \sqrt { 7 } \}$
B) $\{ - 7 i , 7 i \}$
C) $\{ - \sqrt { 7 } , \sqrt { 7 } \}$
D) $\{ - 7,7 \}$

Question 21

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
$$x ^ { 2 } + 14 x$$

A) $x ^ { 2 } + 14 x + 14 = ( x + 196 ) ^ { 2 }$
B) $x ^ { 2 } + 14 x + 196 = ( x + 14 ) ^ { 2 }$
C) $x ^ { 2 } + 14 x + 49 = ( x + 7 ) ^ { 2 }$
D) $x ^ { 2 } + 14 x + 7 = ( x + 49 ) ^ { 2 }$

Question 22

Solve the equation by completing the square.
$$x ^ { 2 } + x + 2 = 0$$

A) $\left\{ \frac { 1 - \mathrm { i } \sqrt { 7 } } { 2 } , \frac { 1 + \mathrm { i } \sqrt { 7 } } { 2 } \right\}$
B) $\left\{ \frac { 1 - \sqrt { 7 } } { 2 } , \frac { 1 + \sqrt { 7 } } { 2 } \right\}$
C) $\left\{ \frac { - 1 - \sqrt { 7 } } { 2 } , \frac { - 1 + \sqrt { 7 } } { 2 } \right\}$
D) $\left\{ \frac { - 1 - \mathrm { i } \sqrt { 7 } } { 2 } , \frac { - 1 + \mathrm { i } \sqrt { 7 } } { 2 } \right\}$

Question 23

Solve the equation by completing the square.
$$x ^ { 2 } + 5 x - 5 = 0$$

A) $\left\{ \frac { - 5 - 3 \sqrt { 5 } } { 2 } , \frac { - 5 + 3 \sqrt { 5 } } { 2 } \right\}$
B) $\left\{ \frac { - 5 - 3 \sqrt { 5 } } { 2 } \right\}$
C) $\{ - 5 - 3 \sqrt { 5 } , - 5 + 3 \sqrt { 5 } \}$
D) $\left\{ \frac { 5 + 3 \sqrt { 5 } } { 2 } \right\}$

Question 24

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
$$x ^ { 2 } - 13 x$$

A) $x ^ { 2 } - 13 x + \frac { 13 } { 2 } = \left( x - \frac { 13 } { 2 } \right) ^ { 2 }$
B) $x ^ { 2 } - 13 x - \frac { 169 } { 4 } = \left( x - \frac { 13 } { 2 } \right) ^ { 2 }$
C) $x ^ { 2 } - 13 x + 169 = ( x - 13 ) ^ { 2 }$
D) $x ^ { 2 } - 13 x + \frac { 169 } { 4 } = \left( x - \frac { 13 } { 2 } \right) ^ { 2 }$

Question 25

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
$$x ^ { 2 } - \frac { 2 } { 9 } x$$

A) $x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 2 } { 81 } = \left( x - \frac { 1 } { 9 } \right) ^ { 2 }$
B) $x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 1 } { 81 } = \left( x - \frac { 1 } { 9 } \right) ^ { 2 }$
C) $x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 1 } { 81 } = \left( x + \frac { 1 } { 9 } \right) ^ { 2 }$
D) $x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 4 } { 81 } = \left( x - \frac { 2 } { 9 } \right) ^ { 2 }$

Question 26

Solve the equation by completing the square.
$$x ^ { 2 } + 10 x + 6 = 0$$

A) $\{ 5 - \sqrt { 6 } , 5 + \sqrt { 6 } \}$
B) $\{ - 10 + \sqrt { 6 } \}$
C) $\{ 5 + \sqrt { 19 } \}$
D) $\{ - 5 - \sqrt { 19 } , - 5 + \sqrt { 19 } \}$

Question 27

Solve the equation by completing the square.
$$x ^ { 2 } + 14 x = - 26$$

A) $\{ 7 + \sqrt { 23 } \}$
B) $\{ 7 - \sqrt { 26 } , 7 + \sqrt { 26 } \}$
C) $\{ - 14 + \sqrt { 26 } \}$
D) $\{ - 7 - \sqrt { 23 } , - 7 + \sqrt { 23 } \}$

Question 28

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
$$\mathrm { p } ^ { 2 } + 5 \mathrm { p }$$

A) $p ^ { 2 } + 5 p + \frac { 25 } { 4 } = \left( p + \frac { 5 } { 2 } \right) ^ { 2 }$
B) $\mathrm { p } ^ { 2 } + 5 \mathrm { p } - \frac { 25 } { 4 } = \left( \mathrm { p } - \frac { 5 } { 2 } \right) ^ { 2 }$
C) $p ^ { 2 } + 5 p + 10 = ( p + 5 ) ^ { 2 }$
D) $p ^ { 2 } + 5 p + \frac { 25 } { 2 } = \left( p + \frac { 25 } { 2 } \right) ^ { 2 }$

Question 29

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
$$y ^ { 2 } - 10 y$$

A) $y ^ { 2 } - 10 y + 25 = ( y - 5 ) ^ { 2 }$
B) $y ^ { 2 } - 10 y - 100 = ( y - 10 ) ^ { 2 }$
C) $y ^ { 2 } - 10 y - 25 = ( y - 5 ) ^ { 2 }$
D) $y ^ { 2 } - 10 y + 100 = ( y - 10 ) ^ { 2 }$

Question 30

Solve the equation by completing the square.
$$2 x ^ { 2 } - 3 x = 5$$

A) $\left\{ \frac { 5 } { 2 } , 1 \right\}$
B) $\left\{ \frac { 5 } { 2 } , - 1 \right\}$
C) $\left\{ \frac { 2 } { 5 } , - 1 \right\}$
D) $\left\{ \frac { 2 } { 5 } , 1 \right\}$

Question 31

Solve the equation by completing the square.
$$x ^ { 2 } + 6 x = 31$$

A) $\{ - 3 - 2 \sqrt { 10 } , - 3 + 2 \sqrt { 10 } \}$
B) $\{ - 3 - 2 \sqrt { 20 } , - 3 + 2 \sqrt { 20 } \}$
C) $\{ 2 \sqrt { 10 } - 3,2 \sqrt { 10 } + 3 \}$
D) $\{ - 2 \sqrt { 10 } , 2 \sqrt { 10 } \}$

Question 32

Solve the equation by completing the square.
$$49 x ^ { 2 } + 98 x + 13 = 0$$

A) $\left\{ \frac { 1 } { 7 } , \frac { 13 } { 7 } \right\}$
B) $\left\{ - \frac { 1 } { 49 } , - \frac { 13 } { 49 } \right\}$
C) $\left\{ - \frac { 13 } { 49 } , \frac { 26 } { 49 } \right\}$
D) $\left\{ - \frac { 1 } { 7 } , - \frac { 13 } { 7 } \right\}$

Question 33

Solve the equation by completing the square.
$$x ^ { 2 } + 8 x = 5$$

A) $\{ - 4 - \sqrt { 21 } , - 4 + \sqrt { 21 } \}$
B) $\{ - 1 - \sqrt { 21 } , - 1 + \sqrt { 21 } \}$
C) $\{ - 4 - 2 \sqrt { 21 } , - 4 + 2 \sqrt { 21 } \}$
D) $\{ 4 + \sqrt { 21 } \}$

Question 34

Solve the equation by completing the square.
$$x ^ { 2 } + 4 x + 3 = 0$$

A) $\{ - 1 , - 3 \}$
B) $\{ 1 , - 1 \}$
C) $\{ 6 , - 3 \}$
D) $\{ 1,3 \}$

Question 35

Solve the equation by completing the square.
$$x ^ { 2 } + 18 x = - 58$$

A) $\{ - 18 + \sqrt { 58 } \}$
B) $\{ - 9 - \sqrt { 23 } , - 9 + \sqrt { 23 } \}$
C) $\{ 9 + \sqrt { 23 } \}$
D) $\{ 9 - \sqrt { 58 } , 9 + \sqrt { 58 } \}$

Question 36

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
$$x ^ { 2 } + \frac { 4 } { 9 } x$$

A) $x ^ { 2 } + \frac { 4 } { 9 } x + \frac { 2 } { 81 } = \left( x + \frac { 2 } { 9 } \right) ^ { 2 }$
B) $x ^ { 2 } + \frac { 4 } { 9 } x + \frac { 4 } { 9 } = \left( x + \frac { 2 } { 9 } \right) ^ { 2 }$
C) $x ^ { 2 } + \frac { 4 } { 9 } x + \frac { 4 } { 81 } = \left( x + \frac { 2 } { 9 } \right) ^ { 2 }$
D) $x ^ { 2 } + \frac { 4 } { 9 } x + \frac { 8 } { 81 } = \left( x + \frac { 4 } { 9 } \right) ^ { 2 }$

Question 37

Solve the equation by completing the square.
$$x ^ { 2 } + 62 = - 18 x$$

A) $\{ - 9 - \sqrt { 19 } , - 9 + \sqrt { 19 } \}$
B) $\{ - 18 + \sqrt { 62 } \}$
C) $\{ 9 + \sqrt { 19 } \}$
D) $\{ 9 - \sqrt { 62 } , 9 + \sqrt { 62 } \}$

Question 38

Solve the equation by completing the square.
$$16 x ^ { 2 } - 7 x + 1 = 0$$

A) $\left\{ \frac { 7 - \mathrm { i } \sqrt { 15 } } { 32 } , \frac { - 7 + \mathrm { i } \sqrt { 15 } } { 32 } \right\}$
B) $\left\{ \frac { 7 - i \sqrt { 15 } } { 32 } , \frac { 7 + i \sqrt { 15 } } { 32 } \right\}$
C) $\left\{ \frac { - 7 - \mathrm { i } \sqrt { 15 } } { 32 } , \frac { 7 + \mathrm { i } \sqrt { 15 } } { 32 } \right\}$
D) $\left\{ \frac { - 7 - \mathrm { i } \sqrt { 15 } } { 32 } , \frac { - 7 + \mathrm { i } \sqrt { 15 } } { 32 } \right\}$

Question 39

Solve the equation by completing the square.
$$x ^ { 2 } + 4 x + 20 = 0$$

A) $\{ - 6,2 \}$
B) $\{ - 2 - 4 i , - 2 + 4 i \}$
C) $\{ - 2 + 4 i \}$
D) $\{ - 2 - 16 i , - 2 + 16 i \}$

Question 40

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
$$x ^ { 2 } + \frac { 1 } { 6 } x$$

A) $x ^ { 2 } + \frac { 1 } { 6 } x + 144 = ( x + 12 ) ^ { 2 }$
B) $x ^ { 2 } + \frac { 1 } { 6 } x + \frac { 1 } { 144 } = \left( x + \frac { 1 } { 12 } \right) ^ { 2 }$
C) $x ^ { 2 } + \frac { 1 } { 6 } x + \frac { 1 } { 36 } = \left( x + \frac { 1 } { 6 } \right) ^ { 2 }$
D) $x ^ { 2 } + \frac { 1 } { 6 } x + \frac { 1 } { 12 } = \left( x + \frac { 1 } { 6 } \right) ^ { 2 }$

Question 41

Solve the equation by completing the square.
$$x ^ { 2 } + 2 = - x$$

A) $\left\{ \frac { 1 - \mathrm { i } \sqrt { 7 } } { 2 } , \frac { 1 + \mathrm { i } \sqrt { 7 } } { 2 } \right\}$
B) $\left\{ \frac { - 1 - i \sqrt { 7 } } { 2 } , \frac { - 1 + i \sqrt { 7 } } { 2 } \right\}$
C) $\left\{ \frac { - 1 - \sqrt { 7 } } { 2 } , \frac { - 1 + \sqrt { 7 } } { 2 } \right\}$
D) $\left\{ \frac { 1 - \sqrt { 7 } } { 2 } , \frac { 1 + \sqrt { 7 } } { 2 } \right\}$

Question 42

Use the quadratic formula to solve the equation.
$$3 x ^ { 2 } + 12 x + 1 = 0$$

A) $\left\{ \frac { - 6 - \sqrt { 33 } } { 6 } , \frac { - 6 + \sqrt { 33 } } { 6 } \right\}$
B) $\left\{ \frac { - 12 - \sqrt { 33 } } { 3 } , \frac { - 12 + \sqrt { 33 } } { 3 } \right\}$
C) $\left\{ \frac { - 6 - \sqrt { 39 } } { 3 } , \frac { - 6 + \sqrt { 39 } } { 3 } \right\}$
D) $\left\{ \frac { - 6 - \sqrt { 33 } } { 3 } , \frac { - 6 + \sqrt { 33 } } { 3 } \right\}$

Question 43

Use the quadratic formula to solve the equation.
$$\mathrm { y } ^ { 2 } - 18 \mathrm { y } + 81 = 0$$

A) $\{ - 9,9 \}$
B) $\{ - 9 - i , - 9 + i \}$
C) $\{ - 9 \}$
D) $\{ 9 \}$

Question 44

Solve.
Use the formula $\mathrm { A } = \mathrm { P } ( 1 + \mathrm { r } ) ^ { \mathrm { t } }$ . Find the rate, $\mathrm { r }$ , at which $\$ 1400$ grows to $\$ 1573$ in 2 years.

A) $7 \%$
B) $5 \%$
C) $6 \%$
D) $12 \%$

Question 45

Use the quadratic formula to solve the equation.
$$2 y ^ { 2 } - 7 y - 9 = 0$$

A) $\left\{ \frac { 2 } { 9 } , 0 \right\}$
B) $\left\{ \frac { 2 } { 9 } , - 1 \right\}$
C) $\left\{ \frac { 2 } { 9 } , 1 \right\}$
D) $\left\{ \frac { 9 } { 2 } , - 1 \right\}$

Question 46

Solve.
A common equation used in business is a demand equation. It expresses the relationship between the unit price of some commodity and the quantity demanded. In the demand equation $p = - x ^ { 2 } + 107$ , for a certain style of calculator, $\mathrm { p }$ is the price per calculator in dollars and $\mathrm { x }$ is the quantity demanded in thousands. Find the demand for the calculator if the price is $\$ 7$ per calculator.

A) 11 thousand units
B) 58 thousand units
C) 50 thousand units
D) 10 thousand units

Question 47

Solve.
The area of a square porch is 121 square feet. Find the dimensions of the porch.

A) 10 feet by 10 feet
B) 13 feet by 13 feet
C) 12 feet by 12 feet
D) 11 feet by 11 feet

Question 48

Use the quadratic formula to solve the equation.
$$x ^ { 2 } - 2 x - 15 = 0$$

A) $\{ 3,5 \}$
B) $\{ - 3,5 \}$
C) $\{ 3 , - 5 \}$
D) $\{ - 15,0 \}$

Question 49

Solve.
The distance, $s ( t )$ , in feet traveled by a freely falling object is given by the function $s ( t ) = 16 t ^ { 2 }$ , where $t$ is time in seconds. Use this formula to find the time it would take for an object to fall to the ground from a cliff that is 144 feet high.

A) 9 seconds
B) 4 seconds
C) 2 seconds
D) 3 seconds

Question 50

Solve.
An isosceles right triangle has legs of equal length. If the hypotenuse is 22 inches long, find the length of each leg.

A) $\frac { 11 } { 2 } \sqrt { 2 } \mathrm { in }$ .
B) $22 \sqrt { 2 } \mathrm { in }$ .
C) $121 \sqrt { 2 } \mathrm { in }$ .
D) $11 \sqrt { 2 } \mathrm { in }$ .

Question 51

Use the quadratic formula to solve the equation.
$$x ^ { 2 } + 4 x + 40 = 0$$

A) $\{ - 2 - 6 i , - 2 + 6 i \}$
B) $\{ - 2 - 36 i , - 2 + 36 i \}$
C) $\{ - 8,4 \}$
D) $\{ - 2 + 6 i \}$

Question 52

Solve the equation by completing the square.
$$2 x ^ { 2 } + 12 x + 3 = 0$$

A) $\left\{ \frac { - 12 - \sqrt { 30 } } { 2 } , \frac { - 12 + \sqrt { 30 } } { 2 } \right\}$
B) $\left\{ \frac { - 6 - \sqrt { 30 } } { 2 } , \frac { - 6 + \sqrt { 30 } } { 2 } \right\}$
C) $\left\{ \frac { - 6 - \sqrt { 30 } } { 4 } , \frac { - 6 + \sqrt { 30 } } { 4 } \right\}$
D) $\left\{ \frac { - 6 - \sqrt { 42 } } { 2 } , \frac { - 6 + \sqrt { 42 } } { 2 } \right\}$

Question 53

Use the quadratic formula to solve the equation.
$5 x ^ { 2 } + 7 x + 9 = 0$

A) $\left\{ \frac { - 7 - \sqrt { 131 } } { 10 } , \frac { - 7 + \sqrt { 131 } } { 10 } \right\}$
B) $\left\{ \frac { 7 - \mathrm { i } \sqrt { 131 } } { 10 } , \frac { 7 + \mathrm { i } \sqrt { 131 } } { 10 } \right\}$
C) $\left\{ \frac { - 7 - \mathrm { i } \sqrt { 131 } } { 10 } , \frac { - 7 + \mathrm { i } \sqrt { 131 } } { 10 } \right\}$
D) $\left\{ \frac { 7 - \sqrt { 131 } } { 10 } , \frac { 7 + \sqrt { 131 } } { 10 } \right\}$

Question 54

Use the quadratic formula to solve the equation.
$$4 x ^ { 2 } + 10 x = - 3$$

A) $\left\{ \frac { - 5 - \sqrt { 13 } } { 8 } , \frac { - 5 + \sqrt { 13 } } { 8 } \right\}$
В) $\left\{ \frac { - 10 - \sqrt { 13 } } { 4 } , \frac { - 10 + \sqrt { 13 } } { 4 } \right\}$
C) $\left\{ \frac { - 5 - \sqrt { 37 } } { 4 } , \frac { - 5 + \sqrt { 37 } } { 4 } \right\}$
D) $\left\{ \frac { - 5 - \sqrt { 13 } } { 4 } , \frac { - 5 + \sqrt { 13 } } { 4 } \right\}$

Question 55

Solve the equation by completing the square.
$$4 \mathrm { x } ^ { 2 } + 1 = 3 \mathrm { x }$$

A) $\left\{ \frac { 3 - i \sqrt { 7 } } { 8 } , \frac { - 3 + i \sqrt { 7 } } { 8 } \right\}$
B) $\left\{ \frac { 3 - i \sqrt { 7 } } { 8 } , \frac { 3 + i \sqrt { 7 } } { 8 } \right\}$
C) $\left\{ \frac { - 3 - \mathrm { i } \sqrt { 7 } } { 8 } , \frac { - 3 + \mathrm { i } \sqrt { 7 } } { 8 } \right\}$
D) $\left\{ \frac { - 3 - \mathrm { i } \sqrt { 7 } } { 8 } , \frac { 3 + \mathrm { i } \sqrt { 7 } } { 8 } \right\}$

Question 56

Use the quadratic formula to solve the equation.
$$x ^ { 2 } + 16 x + 64 = 0$$

A) $\{ - 8 \}$
B) $\{ 8 - \mathrm { i } , 8 + \mathrm { i } \}$
C) $\{ - 8,8 \}$
D) $\{ 8 \}$

Question 57

Use the quadratic formula to solve the equation.
$$n ^ { 2 } + 16 n + 43 = 0$$

A) $\{ - 8 - \sqrt { 21 } , - 8 + \sqrt { 21 } \}$
B) $\{ - 16 + \sqrt { 43 } \}$
C) $\{ 8 - \sqrt { 43 } , 8 + \sqrt { 43 } \}$
D) $\{ 8 + \sqrt { 21 } \}$

Question 58

Use the quadratic formula to solve the equation.
$16 \mathrm { x } ^ { 2 } + 1 = 5 \mathrm { x }$

A) $\left\{ \frac { - 5 - i \sqrt { 39 } } { 32 } , \frac { 5 + i \sqrt { 39 } } { 32 } \right\}$
B) $\left\{ \frac { - 5 - i \sqrt { 39 } } { 32 } , \frac { - 5 + i \sqrt { 39 } } { 32 } \right\}$
C) $\left\{ \frac { 5 - i \sqrt { 39 } } { 32 } , \frac { 5 + i \sqrt { 39 } } { 32 } \right\}$
D) $\left\{ \frac { 5 - \mathrm { i } \sqrt { 39 } } { 32 } , \frac { - 5 + \mathrm { i } \sqrt { 39 } } { 32 } \right\}$

Question 59

Use the quadratic formula to solve the equation.
$$6 x ^ { 2 } + 24 x = - 19$$

A) $\left\{ \frac { - 12 - \sqrt { 30 } } { 6 } , \frac { - 12 + \sqrt { 30 } } { 6 } \right\}$
B) $\left\{ \frac { - 12 - \sqrt { 258 } } { 6 } , \frac { - 12 + \sqrt { 258 } } { 6 } \right\}$
C) $\left\{ \frac { - 12 - \sqrt { 30 } } { 12 } , \frac { - 12 + \sqrt { 30 } } { 12 } \right\}$
D) $\left\{ \frac { - 24 - \sqrt { 30 } } { 6 } , \frac { - 24 + \sqrt { 30 } } { 6 } \right\}$

Question 60

Use the quadratic formula to solve the equation.
$$4 x ^ { 2 } = - 10 x - 3$$

A) $\left\{ \frac { - 5 - \sqrt { 37 } } { 4 } , \frac { - 5 + \sqrt { 37 } } { 4 } \right\}$
B) $\left\{ \frac { - 10 - \sqrt { 13 } } { 4 } , \frac { - 10 + \sqrt { 13 } } { 4 } \right\}$
C) $\left\{ \frac { - 5 - \sqrt { 13 } } { 4 } , \frac { - 5 + \sqrt { 13 } } { 4 } \right\}$
D) $\left\{ \frac { - 5 - \sqrt { 13 } } { 8 } , \frac { - 5 + \sqrt { 13 } } { 8 } \right\}$

Question 61

Use the quadratic formula to solve the equation.
$$( x - 3 ) ( 2 x + 2 ) = 3 ( x - 1 ) - 6$$

A) $\left\{ \frac { 7 } { 4 } - \frac { \sqrt { 73 } } { 4 } , \frac { 7 } { 4 } + \frac { \sqrt { 73 } } { 4 } \right\}$
B) $\left\{ - 3 , - \frac { 1 } { 2 } \right\}$
C) $\left\{ - \frac { 7 } { 4 } - \frac { \sqrt { 73 } } { 4 } , - \frac { 7 } { 4 } + \frac { \sqrt { 73 } } { 4 } \right\}$
D) $\left\{ \frac { 1 } { 2 } , 3 \right\}$

Question 62

Solve.
A ball is thrown upward with an initial velocity of 35 meters per second from a cliff that is 70 meters high. The height of the ball is given by the quadratic equation $h = - 4.9 t ^ { 2 } + 35 t + 100$ where $h$ is in meters and $t$ is the time in seconds since the ball was thrown. Find the time that the ball will be 30 meters from the ground. Round your answer to the nearest tenth of a second.

A) $9.4$ seconds
B) $9.3$ seconds
C) $8.8$ seconds
D) $8.9$ seconds

Question 63

Use the discriminant to determine the number and type of solutions of the equation.
$$x ^ { 2 } - 8 = 0$$

A) Two real solutions
B) Two complex but not real solutions
C) One real solution

Question 64

Use the quadratic formula to solve the equation.
$$\frac { 1 } { 10 } x ^ { 2 } + x + 1 = 0$$

A) $\{ - 10 + \sqrt { 10 } \}$
B) $\{ 5 - \sqrt { 10 } , 5 + \sqrt { 10 } \}$
C) $\{ 5 + \sqrt { 15 } \}$
D) $\{ - 5 - \sqrt { 15 } , - 5 + \sqrt { 15 } \}$

Question 65

Use the discriminant to determine the number and type of solutions of the equation.
$$x ^ { 2 } - 4 x - 1 = 0$$

A) One real solution
B) Two complex but not real solutions
C) Two real solutions

Question 66

Solve.
A ball is thrown downward with an initial velocity of 42 meters per second from a cliff that is 100 meters high. The height of the ball is given by the quadratic equation $h = - 4.9 t ^ { 2 } - 42 t + 120$ where $h$ is in meters and $t$ is the time in seconds since the ball was thrown. Find the time that the ball will be 20 meters from the ground. Round your answer to the nearest tenth of a second.

A) $2.0$ seconds
B) $1.8$ seconds
C) $2.9$ seconds
D) $1.9$ seconds

Question 67

Use the quadratic formula to solve the equation.
$$2 y - \frac { 3 } { 5 } = \frac { 3 } { 5 } y ^ { 2 }$$

A) $\{ 3 \}$
B) $\left\{ \frac { 5 - i \sqrt { 34 } } { 3 } , \frac { 5 + i \sqrt { 34 } } { 3 } \right\}$
C) $\left\{ \frac { 1 } { 3 } , 3 \right\}$
D) $\left\{ \frac { 10 - \sqrt { 76 } } { 6 } , \frac { 10 + \sqrt { 76 } } { 6 } \right\}$

Question 68

Use the discriminant to determine the number and type of solutions of the equation.
$$x ^ { 2 } + 6 x - 7 = 0$$

A) Two real solutions
B) Two complex but not real solutions
C) One real solution

Question 69

Use the quadratic formula to solve the equation.
$$\frac { 1 } { 2 } x ^ { 2 } + \frac { 1 } { 4 } x - \frac { 1 } { 2 } = 0$$

A) $\left\{ \frac { - 1 - i \sqrt { 15 } } { 4 } , \frac { - 1 + i \sqrt { 15 } } { 4 } \right\}$
B) $\{ - 1 \}$
C) $\left\{ - \frac { 5 } { 4 } , \frac { 3 } { 4 } \right\}$
D) $\left\{ \frac { - 1 - \sqrt { 17 } } { 4 } , \frac { - 1 + \sqrt { 17 } } { 4 } \right\}$

Question 70

Use the quadratic formula to solve the equation.
$$\frac { z ^ { 2 } } { 2 } = \frac { z } { 7 } + \frac { 9 } { 14 }$$

A) $\left\{ - \frac { 9 } { 7 } , - 1 \right\}$
В) $\left\{ - 1 , \frac { 9 } { 7 } \right\}$
C) $\left\{ - \frac { 9 } { 7 } , 1 \right\}$
D) $\left\{ \frac { 9 } { 7 } \right\}$

Question 71

Solve.
A ball is thrown downward with an initial velocity of 28 meters per second from a cliff that is 110 meters high. The height of the ball is given by the quadratic equation $h = - 4.9 t ^ { 2 } - 28 t + 110$ where $h$ is in meters and $t$ is the time in seconds since the ball was thrown. Find the time it takes the ball to hit the ground. Round your answer to the nearest tenth of a second.

A) $2.6$ seconds
B) $2.8$ seconds
C) $3.7$ seconds
D) $2.7$ seconds

Question 72

Use the quadratic formula to solve the equation.
$$( x + 8 ) ( x - 1 ) = 9$$

A) $\left\{ \frac { - 7 - 3 \sqrt { 13 } } { 2 } , \frac { - 7 + 3 \sqrt { 13 } } { 2 } \right\}$
B) $\left\{ \frac { - 7 - 3 i \sqrt { 13 } } { 2 } , \frac { - 7 + 3 i \sqrt { 13 } } { 2 } \right\}$
C) $\left\{ \frac { 7 - 3 i \sqrt { 13 } } { 2 } , \frac { 7 + 3 i \sqrt { 13 } } { 2 } \right\}$
D) $\left\{ \frac { 7 - 3 \sqrt { 13 } } { 2 } , \frac { 7 + 3 \sqrt { 13 } } { 2 } \right\}$

Question 73

Use the quadratic formula and a calculator to approximate the solution to the nearest tenth.
$$- 2 x ^ { 2 } + 6 x + 3 = 0$$

A) $\{ - 3.4,0.4 \}$
В) $\{ - 0.9,6.9 \}$
C) $\{ - 0.4,3.4 \}$
D) $\{ - 13.5,16.5 \}$

Question 74

Solve.
The revenue for a small company is given by the quadratic function $r ( t ) = 6 t ^ { 2 } + 4 t + 550$ where $t$ is the number of years since 2010 and $r ( t )$ is in thousands of dollars. If this trend continues, find the year after 2010 in which the company's revenue will be $\$ 872$ thousand. Round to the nearest whole year.

A) 2024
B) 2018
C) 2019
D) 2017

Question 75

Use the discriminant to determine the number and type of solutions of the equation.
$$10 - 8 x ^ { 2 } = - 6 x + 9$$

A) Two complex but not real solutions
B) Two real solutions
C) One real solution

Question 76

Solve.
A ball is thrown upward with an initial velocity of 42 meters per second from a cliff that is 30 meters high. The height of the ball is given by the quadratic equation $\mathrm { h } = - 4.9 \mathrm { t } ^ { 2 } + 42 \mathrm { t } + 30$ where $\mathrm { h }$ is in meters and $\mathrm { t }$ is the time in seconds since the ball was thrown. Find the time it takes the ball to hit the ground. Round your answer to the nearest tenth of a second.

A) $9.2$ seconds
B) $9.8$ seconds
C) $15.2$ seconds
D) $8.6$ seconds

Question 77

Use the quadratic formula to solve the equation.
$$x ^ { 2 } + 14 x + 85 = 0$$

A) $\{ - 7 - 36 i , - 7 + 36 i \}$
B) $\{ - 7 - 6 i , - 7 + 6 i \}$
C) $\{ - 7 + 6 i \}$
D) $\{ - 13 , - 1 \}$

Question 78

Use the quadratic formula to solve the equation.
$$x ( x - 6 ) = 8$$

A) $\{ 3 - \sqrt { 17 } , 3 + \sqrt { 17 } \}$
B) $\{ - 3 + 1 , - 3 - 1 \}$
C) $\{ 3 - 1,3 + 1 \}$
D) $\{ - 3 + \sqrt { 17 } , - 3 - \sqrt { 17 } \}$

Question 79

Use the quadratic formula to solve the equation.
$$x ( 5 x + 9 ) = 4$$

A) $\left\{ \frac { - 9 - 1 } { 10 } , \frac { - 9 + 1 } { 10 } \right\}$
B) $\left\{ \frac { 9 - 1 } { 10 } , \frac { 9 + 1 } { 10 } \right\}$
C) $\left\{ \frac { - 9 - \sqrt { 161 } } { 10 } , \frac { - 9 + \sqrt { 161 } } { 10 } \right\}$
D) $\left\{ \frac { 9 - \sqrt { 161 } } { 10 } , \frac { 9 + \sqrt { 161 } } { 10 } \right\}$

Question 80

Use the quadratic formula to solve the equation.
$$( x + 3 ) ( x - 1 ) = 0$$

A) $\{ 1 - 1,1 + 1 \}$
В) $[ - 1 - \sqrt { 7 } , - 1 + \sqrt { 7 } \}$
C) $\{ - 1 - 1 , - 1 + 1 \}$
D) $\{ 1 - \sqrt { 7 } , 1 + \sqrt { 7 } \}$