Deck 16: Quadratic Equations and Nonlinear Graphs

Question 1

Use the square root property to solve the quadratic equation.

- $2 x ^ { 2 } = 3$

A) $\frac { \sqrt { 6 } } { 2 }$
B) $\pm \frac { 3 } { 2 }$
C) $\pm \frac { \sqrt { 6 } } { 2 }$
D) $\frac { \sqrt { 3 } } { 2 }$

Answer 1

$\pm \frac { \sqrt { 6 } } { 2 }$

Question 2

Use the square root property to solve the quadratic equation.

- $5 x ^ { 2 } = 16$

A) $\frac { 4 \sqrt { 5 } } { 5 }$
B) $\pm \frac { 4 \sqrt { 5 } } { 5 }$
C) $\pm \frac { \sqrt { 80 } } { 5 }$
D) $\pm \frac { 4 } { 5 }$

Answer 2

$\pm \frac { 4 \sqrt { 5 } } { 5 }$

Question 3

Solve the equation by factoring.

- $5 x ^ { 2 } - 80 = 0$

A)4
B)±20
C)±4
D)8

Answer 3

±4

Question 4

Use the square root property to solve the quadratic equation.

- $( x - 4 ) ^ { 2 } = 49$

A)7, -7
B)53
C)11, -3
D)-3, -11

Question 5

Use the square root property to solve the quadratic equation.

- $x ^ { 2 } = - 4$

A)No real solution
B) $\pm 16$
C) $\pm 2$
D)- 2

Question 6

Solve the equation by factoring.

- $x ^ { 2 } - 25 = 0$

A)12.5
B)5
C) $\pm 5$
D) $\pm 6$

Question 7

Solve the equation by factoring.

- $x ^ { 2 } + 12 x = - 27$

A)-9, -3
B)3, 9
C)-27, -1
D)-9, 3

Question 8

Solve the equation by factoring.

- $x ^ { 2 } - 49 = 48 x$

A)-1, 49
B)1, -49
C)-7, 7
D)-7

Question 9

Use the square root property to solve the quadratic equation.

- $x ^ { 2 } = 14$

A)7
B) $\sqrt { 14 }$
C) $\pm 196$
D) $\pm \sqrt { 14 }$

Question 10

Solve the equation by factoring.

- $20 x ^ { 2 } - 4 x = 0$

A) $\frac { 1 } { 5 }$
B) $\frac { 1 } { 5 } , 0$
C)0
D) $\frac { 1 } { 5 } , 4$

Question 11

Use the square root property to solve the quadratic equation.

- $x ^ { 2 } = \frac { 1 } { 49 }$

A) $\frac { 1 } { 7 }$
B) $\pm \frac { 1 } { 2401 }$
C) $\pm \frac { 1 } { 7 }$
D) $\pm 7$

Question 12

Solve the equation by factoring.

- $6 x ^ { 2 } + 11 x = 0$

A)0
B) $- \frac { 11 } { 6 } , 11$
C) $- \frac { 11 } { 6 } , 0$
D) $- \frac { 11 } { 6 }$

Question 13

Solve the equation by factoring.

- $x ^ { 2 } + 6 x = 16$

A)-8, 1
B)8, -2
C)8, 2
D)-8, 2

Question 14

Use the square root property to solve the quadratic equation.

- $( \mathrm { r } + 5 ) ^ { 2 } = 11$

A)- $- 5 \pm \sqrt { 11 }$
B) $\pm \sqrt { 11 }$
C) $5 \pm \sqrt { 11 }$
D)6

Question 15

Solve the equation by factoring.

- $x ^ { 2 } + 7 x - 44 = 0$

A)11, -4
B)-11, 1
C)-11, 4
D)11, 4

Question 16

Use the square root property to solve the quadratic equation.

- $( x + 7 ) ^ { 2 } = 12$

A) $- 7 \pm 2 \sqrt { 3 }$
B) $2 \sqrt { 3 } \pm 7$
C) $\pm 2 \sqrt { 3 }$
D) $- 7 \pm 2 \sqrt { 6 }$

Question 17

Solve the equation by factoring.

- $12 y ^ { 2 } + 25 y + 12 = 0$

A) $\frac { 3 } { 4 } , - \frac { 4 } { 3 }$
B)- $- \frac { 1 } { 4 } , - \frac { 1 } { 3 }$
C) $- \frac { 3 } { 4 } , - \frac { 4 } { 3 }$
D) $\frac { 3 } { 4 } , \frac { 4 } { 3 }$

Question 18

Use the square root property to solve the quadratic equation.

- $x ^ { 2 } = 225$

A)112.5
B) $\pm 15$
C)15
D)±16

Question 19

Use the square root property to solve the quadratic equation.

- $5 x ^ { 2 } - 35 = 0$

A) $\pm \frac { \sqrt { 35 } } { 5 }$
B) $\sqrt { 7 }$
C) $\pm \sqrt { 7 }$
D) $\pm \frac { \sqrt { 175 } } { 5 }$

Question 20

Use the square root property to solve the quadratic equation.

- $x ^ { 2 } - 6 = 0$

A) $\pm 6$
B)No real solution
C) $\sqrt { 6 }$
D) $\pm \sqrt { 6 }$

Question 21

Use the square root property to solve the quadratic equation.

- $( 2 x + 5 ) ^ { 2 } = 49$

A)1, -6
B)0, 1
C)1, 6
D)27, -27

Question 22

Use the square root property to solve the quadratic equation.

- $( 4 x - 7 ) ^ { 2 } = 50$

A) $\frac { 7 \pm 5 \sqrt { 2 } } { 4 }$
B) $\frac { 5 \sqrt { 2 } \pm 7 } { 4 }$
C) $\frac { 7 + 5 \sqrt { 2 } } { 4 }$
D) $\frac { 7 \pm 2 \sqrt { 5 } } { 4 }$

Question 23

Use the square root property to solve the quadratic equation.

- $( 5 x - 2 ) ^ { 2 } = 6$

A) $\frac { - 2 \pm \sqrt { 6 } } { 5 }$
B) $\frac { \sqrt { 6 } \pm 2 } { 5 }$
C) $- \frac { 8 } { 5 } \text { and } \frac { 4 } { 5 }$
D) $\frac { 2 \pm \sqrt { 6 } } { 5 }$

Question 24

Use the square root property to solve the quadratic equation.

- $\left( m - \frac { 1 } { 7 } \right) ^ { 2 } = \frac { 1 } { 49 }$

A) $\pm \frac { 2 } { 7 }$
B) $\frac { 8 } { 49 }$
C) $0 , \frac { 2 } { 7 }$
D) $0 , - \frac { 2 } { 7 }$

Question 25

Use the square root property to solve the quadratic equation.

- $( p - 1 ) ^ { 2 } = - 81$

A)-10, 8
B)-80, 82
C)-8, 10
D)no real solution

Question 26

Solve.

-The strawberry yield (in bushels per acre)for a farm in Springfield from 1996 through 1998 is given by the equationn $y = 9 x ^ { 2 } + 35$ . In this equation, x = 0 represents the year 1997. Assume this trend continues and predict
The year in which the Springfield farm's strawberry yield will be 611 bushels per acre.

A)2007
B)2005
C)2004
D)2006

Question 27

Use the square root property to solve the quadratic equation.

- $( 5 x - 1 ) ^ { 2 } = \frac { 16 } { 25 }$

A)5, -3
B) $- \frac { 4 } { 25 } , \frac { 4 } { 25 }$
C) $- \frac { 4 } { 5 } , \frac { 4 } { 5 }$
D) $\frac { 9 } { 25 } , \frac { 1 } { 25 }$

Question 28

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 equationon $p = - x ^ { 2 } + 88$ , for a certain style of
Calculator, p is the price per calculator in dollars and x is the quantity demanded in thousands. Find the demand
For the calculator if the price is $7 per calculator.

A)9 thousand units
B)10 thousand units
C) $40 \frac { 1 } { 2 }$ thousand units
D)39 thousand units

Question 29

Solve.

-The area of a square is found by the equationquation A $A = s ^ { 2 }$ where s is the length of a side. If the area of a square porch is 81 square feet, find the dimensions of the porch.

A)8 feet by 8 feet
B)9 feet by 9 feet
C)11 feet by 11 feet
D)10 feet by 10 feet

Question 30

Solve.
A 35-inch-square TV is on sale at the local electronics store. If 35 inches is the measure of the diagonal of the screen, use the Pythagorean theorem to find the length of the side of the screen to the nearest tenth of an inch.

A)3 in.
B)5.9 in.
C)612.5 in.
D)24.7 in.

Question 31

Use the square root property to solve the quadratic equation.

- $( 5 x + 4 ) ^ { 2 } = 6$

A) $\frac { 4 \pm \sqrt { 6 } } { 5 }$
B) $\frac { \sqrt { 6 } \pm 4 } { 5 }$
C) $- 2 \text { and } \frac { 2 } { 5 }$
D) $\frac { - 4 \pm \sqrt { 6 } } { 5 }$

Question 32

Determine the number to add to make each expression a perfect square trinomial.

- $x ^ { 2 } + 8 x$

A)16
B)4
C)8
D)64

Question 33

Solve.

-The area of a circle is found by the equationon A $\mathrm { A } = \pi \mathrm { r } ^ { 2 }$ .. If the area a of a certain circle is 64? square inches, find its radius r.

A)128 inches
B) $32 \pi$ inch inches
C)8 inches
D)16 inches

Question 34

Use the square root property to solve the quadratic equation.

-(2 $( 2 m - 1 ) ^ { 2 } = 25$

A)6, -4
B)2, -3
C)4, -6
D)3, -2

Question 35

Solve.

-Neglecting air resistance, the distance d in feet that an object falls in t seconds is given by the equatione equation $d = 16 t ^ { 2 }$ . Use this formula to find the time it would take for an object to fall to the ground from a cliff that is 784 feet high.

A)6 seconds
B)8 seconds
C)49 seconds
D)7 seconds

Question 36

Solve.

-Neglecting air resistance, the distance h traveled by a free-falling object in time t is given by the formula $\mathrm { h } = 16 \mathrm { t } ^ { 2 }$ . U Use this formula to find the time of free fall for a parachutist who falls 2605 feet before opening her parachute. Round your answer to the nearest tenth of a second.

A)204.2 sec
B)3.2 sec
C)81.4 sec
D)12.8 sec

Question 37

Use the square root property to solve the quadratic equation.

- $( 19 - 5 x ) ^ { 2 } - 12 = 0$

A) $\frac { 2 \sqrt { 3 } \pm 19 } { 5 }$
B) $\frac { 19 \pm 2 \sqrt { 3 } } { 5 }$
C) $\frac { - 19 \pm 2 \sqrt { 3 } } { 5 }$
D) $\frac { 19 \pm 3 \sqrt { 2 } } { 5 }$

Question 38

Solve.

-The formula for the area of a square iss A $A = s ^ { 2 }$ where s is the length of a side. Use this formula to find the length of a side of a building which has a square base with an area of 232 square meters. Give your answer in exact
Form and as a decimal rounded to the nearest hundredth of a meter.

A) $2 \sqrt { 58 } \approx 15.23 \text { meters }$
B)53,824 meters
C) $58 \sqrt { 2 } \approx 82.02 \text { meters }$
D) $4 \sqrt { 58 } \approx 30.46 \text { meters }$

Question 39

Use the square root property to solve the quadratic equation.

- $\frac { 1 } { 5 } x ^ { 2 } = 3$

A) $\pm \frac { \sqrt { 15 } } { 5 }$
B) $\pm 225$
C) $\pm \sqrt { 15 }$
D) $\sqrt { 15 }$

Question 40

Use the square root property to solve the quadratic equation.

- $3 x ^ { 2 } = 54$

A) $\pm 2 \sqrt { 3 }$
B) $\pm 9 \sqrt { 2 }$
C) $\pm 3 \sqrt { 2 }$
D) $3 \sqrt { 2 }$

Question 41

Determine the number to add to make each expression a perfect square trinomial.

- $x ^ { 2 } - 20 x$

A)10
B)-100
C)-10
D)100

Question 42

Solve the quadratic equation by completing the square.

- $x ^ { 2 } - 8 x = - 15$

A) $\pm \sqrt { 15 }$
B)-5, -3
C)5, 3
D)12, 3

Question 43

Solve the quadratic equation by completing the square.

- $x ^ { 2 } + 7 x = 3$

A) $- 7 \pm \sqrt { 61 }$
B) $\frac { - 7 \pm 2 \sqrt { 3 } } { 2 }$
C) $\frac { - 7 \pm \sqrt { 61 } } { 2 }$
D) $\frac { 7 \pm \sqrt { 61 } } { 2 }$

Question 44

Solve the quadratic equation by completing the square.

- $p ^ { 2 } - 20 p = 0$

A)-20, 0
B)0, 20
C)100
D) $\pm 10$

Question 45

Solve the quadratic equation by completing the square.

- $x ^ { 2 } - 8 x + 11 = 0$

A) $4 \pm \sqrt { 5 }$
B) $- 8 \pm 2 \sqrt { 5 }$
C) $- 4 \pm \sqrt { 5 }$
D) $8 \pm \sqrt { 5 }$

Question 46

Use the square root property to solve the quadratic equation.

- $3 x ^ { 2 } - 6 = 0$

A) $\sqrt { 2 }$
B) $\pm \frac { \sqrt { 6 } } { 3 }$
C) $\pm \frac { \sqrt { 18 } } { 3 }$
D) $\pm \sqrt { 2 }$

Question 47

Solve the quadratic equation by completing the square.

- $x ^ { 2 } - 9 x - 7 = 0$

A) $\frac { 9 \pm \sqrt { 109 } } { 2 }$
B) $\frac { 9 \pm 2 \sqrt { 7 } } { 2 }$
C) $9 \pm \sqrt { 109 }$
D) $\frac { - 9 \pm \sqrt { 109 } } { 2 }$

Question 48

Solve the quadratic equation by completing the square.

- $x ^ { 2 } + 10 x - 7 = 0$

A) $- 10 \pm 4 \sqrt { 2 }$
B) $- 5 \pm 16 \sqrt { 2 }$
C) $5 \pm 4 \sqrt { 2 }$
D)- $- 5 \pm 4 \sqrt { 2 }$

Question 49

Solve the quadratic equation by completing the square.

- $a ^ { 2 } - 2 a - 48 = 0$

A)-42, -6
B)8, -6
C) $\pm \sqrt { - 48 }$
D)-8, 6

Question 50

Solve the quadratic equation by completing the square.

- $z ^ { 2 } + 4 z - 7 = 0$

A) $- 2 \pm \sqrt { 11 }$
B) $- 2 \pm 2 \sqrt { 11 }$
C) $- 1 \pm \sqrt { 11 }$
D) $2 + \sqrt { 11 }$

Question 51

Use the square root property to solve the quadratic equation.

- $x ^ { 2 } = - 121$

A)± 11
B)No real solution
C)- 11
D) $\pm 14,641$

Question 52

Solve the quadratic equation by completing the square.
x(x + 3)= 88

A)11, 8
B)-11, 8
C)-8, 11
D)-11, 1

Question 53

Solve the quadratic equation by completing the square.

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

A) $\pm 3$
B)-6, 0
C)0, 6
D)9

Question 54

Solve the quadratic equation by completing the square.

- $z ^ { 2 } + 14 z + 39 = 0$

A) $- 14 + \sqrt { 39 }$
B) $7 + \sqrt { 10 }$
C) $7 \pm \sqrt { 39 }$
D) $- 7 \pm \sqrt { 10 }$

Question 55

Solve the quadratic equation by completing the square.

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

A) $- 2 \pm 2 \sqrt { 7 }$
B) $2 + \sqrt { 7 }$
C) $- 1 \pm \sqrt { 7 }$
D) $- 2 \pm \sqrt { 7 }$

Question 56

Solve the quadratic equation by completing the square.
x(x - 4)= 45

A)9, 5
B)-9, 1
C)-9, 5
D)-5, 9

Question 57

Solve the quadratic equation by completing the square.

- $x ^ { 2 } + 4 x - 21 = 0$

A)7, -3
B)-7, 1
C)7, 3
D)-7, 3

Question 58

Solve the quadratic equation by completing the square.

- $x ^ { 2 } + 4 x = 7$

A) $2 + \sqrt { 11 }$
B) $- 1 \pm \sqrt { 11 }$
C) $- 2 \pm \sqrt { 11 }$
D) $- 2 \pm 2 \sqrt { 11 }$

Question 59

Use the square root property to solve the quadratic equation.

- $x ^ { 2 } - 10 = 0$

A) $\pm \sqrt { 10 }$
B) $\sqrt { 10 }$
C)No real solution
D) $\pm 10$

Question 60

Solve the quadratic equation by completing the square.

- $y ^ { 2 } + 3 y - 9 = 0$

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

Question 61

Use the square root property to solve the quadratic equation.

- $6 x ^ { 2 } + 8 x + 1 = 0$

A) $\frac { - 4 \pm \sqrt { 10 } } { 6 }$
B) $\frac { - 4 \pm \sqrt { 22 } } { 6 }$
C) $\frac { - 8 \pm \sqrt { 10 } } { 6 }$
D) $\frac { - 4 \pm \sqrt { 10 } } { 12 }$

Question 62

Use the quadratic formula to solve the quadratic equation.

- $x ^ { 2 } + 2 x = 80$

A)x = -10, 1
B)x = 10, 8
C)x = -10, 8
D)x = 10, -8

Question 63

Use the quadratic formula to solve the quadratic equation.

- $4 x ^ { 2 } - 3 x + 1 = 0$

A) $\frac { 3 \pm \sqrt { 7 } } { 4 }$
B) $\frac { - 3 \pm \sqrt { 7 } } { 8 }$
C) $\frac { 3 \pm \sqrt { 7 } } { 8 }$
D)no real solution

Question 64

Use the quadratic formula to solve the quadratic equation.

- $7 k ^ { 2 } - 3 k - 1 = 0$

A) $k = \frac { 3 \pm \sqrt { 37 } } { 14 }$
B) $\mathrm { k } = \frac { 3 \pm \sqrt { 37 } } { 7 }$
C) $k = \frac { 3 \pm \sqrt { 37 } } { 28 }$
D) $k = \frac { - 3 \pm \sqrt { 37 } } { 14 }$

Question 65

Use the square root property to solve the quadratic equation.

- $2 x ^ { 2 } - 3 x - 5 = 0$

A) $\frac { 2 } { 5 } , - 1$
B) $\frac { 5 } { 2 } , - 1$
C) $\frac { 2 } { 5 } , 0$
D) $\frac { 2 } { 5 } , 1$

Question 66

Use the quadratic formula to solve the quadratic equation.

- $m ^ { 2 } = 5 m - 5$

A) $m = \frac { 5 \pm \sqrt { 5 } } { 2 }$
B) $m = \frac { 5 \pm 3 \sqrt { 5 } } { 2 }$
C) $m = \frac { - 5 \pm \sqrt { 5 } } { 2 }$
D) $m = \frac { - 5 \pm 3 \sqrt { 5 } } { 4 }$

Question 67

Use the square root property to solve the quadratic equation.

- $3 x ^ { 2 } = 25$

A) $\frac { 5 \sqrt { 3 } } { 3 }$
B)± $\pm \frac { 5 \sqrt { 3 } } { 3 }$
C) $\pm \frac { \sqrt { 75 } } { 3 }$
D) $\pm \frac { 5 } { 3 }$

Question 68

Use the quadratic formula to solve the quadratic equation.

- $x ^ { 2 } - x = 42$

A)x = 1, 42
B)x = -6, 7
C)x = 6, 7
D)x = -6, -7

Question 69

Use the square root property to solve the quadratic equation.

- $3 x ^ { 2 } + 3 x = 60$

A)5, -4
B)-5, 12
C)-20, 1
D)-5, 4

Question 70

Use the quadratic formula to solve the quadratic equation.

- $64 x ^ { 2 } - 7 = 0$

A) $x = \frac { 7 } { 64 }$
B) $x = \pm \frac { \sqrt { 7 } } { 8 }$
C) $x = \pm \frac { \sqrt { 7 } } { 64 }$
D) $x = 8 \pm \sqrt { 7 }$

Question 71

Use the square root property to solve the quadratic equation.

- $3 x ^ { 2 } - 21 x = - 30$

A)-2, -5
B)3, 2
C)3, -5
D)2, 5

Question 72

Use the quadratic formula to solve the quadratic equation.

- $x ^ { 2 } - 12 x + 27 = 0$

A)x = -9, -3
B)x = 9, 3
C)x = -9, 3
D)x = 27, 0

Question 73

Use the quadratic formula to solve the quadratic equation.

- $x ^ { 2 } + 3 x - 108 = 0$

A)x = -12, 1
B)x = 12, -9
C)x = 12, 9
D)x = -12, 9

Question 74

Use the square root property to solve the quadratic equation.

- $5 x ^ { 2 } + 15 x + 26 = 0$

A) $\frac { 15 \pm \sqrt { 295 } } { 10 }$
B) $\frac { - 15 \pm \sqrt { 295 } } { 10 }$
C) $\frac { - 15 \pm \sqrt { 295 } } { 5 }$
D)no real solution

Question 75

Use the square root property to solve the quadratic equation.

- $2 x ^ { 2 } = - 4 x + 9$ 9

A) $\frac { - 2 \pm \sqrt { 22 } } { 2 }$
B) $\frac { 2 \pm \sqrt { 22 } } { 4 }$
C) $\frac { 2 \pm \sqrt { 22 } } { 2 }$
D) $\frac { - 2 \pm \sqrt { 22 } } { 4 }$

Question 76

Use the quadratic formula to solve the quadratic equation.

- $5 x ^ { 2 } = 55$

A)x = 12
B)x = ± 11
C)x = ±11
D)x = 27.5

Question 77

Use the square root property to solve the quadratic equation.

- $2 x ^ { 2 } - 4 x + 9 = 0$

A) $\frac { 2 \pm \sqrt { 14 } } { 4 }$
B) $\frac { 2 \pm \sqrt { 14 } } { 2 }$
C) $\frac { - 2 \pm \sqrt { 14 } } { 2 }$
D)no real solution

Question 78

Use the square root property to solve the quadratic equation.

- $3 x ^ { 2 } = - 6 x - 2$

A) $\frac { - 6 \pm \sqrt { 3 } } { 3 }$
B) $\frac { - 3 \pm \sqrt { 3 } } { 3 }$
C) $\frac { - 3 \pm \sqrt { 3 } } { 6 }$
D) $\frac { - 3 \pm \sqrt { 15 } } { 3 }$

Question 79

Use the quadratic formula to solve the quadratic equation.

- $x ^ { 2 } - 3 x = 88$

A)x = -11, 1
B)x = -11, 8
C)x = 11, -8
D)x = 11, 8

Question 80

Use the square root property to solve the quadratic equation.

- $3 y ^ { 2 } + 12 y + 7 = 0$

A) $- 2 \pm \frac { \sqrt { 15 } } { 3 }$
B) $- 2 \pm \frac { \sqrt { 15 } } { 6 }$
C) $2 \pm \frac { \sqrt { 15 } } { 6 }$
D) $2 \pm \frac { \sqrt { 15 } } { 3 }$