Deck 8: Quadratic Equations, Functions, and Inequalities

Question 1

Solve the equation $7 x ^ { 2 } = 63$ by using the Square Root Property.

A) $\pm 7$
B) $\pm 3$
C) $\pm 9$
D) $7,3$
E) 9

Answer 1

$\pm 3$

Question 2

Find all real and complex solutions of the quadratic equation $( p - 3 ) ^ { 2 } - 243 = 0$ .

A) $- 9 \pm 3 \sqrt { 3 }$
B) $- 3 \pm 3 \sqrt { 3 } i$
C) $- 3 \pm 9 \sqrt { 3 } i$
D) $9 \pm 3 \sqrt { 3 }$
E) $3 \pm 9 \sqrt { 3 }$

Answer 2

$3 \pm 9 \sqrt { 3 }$

Question 3

Solve $x ^ { 2 } - 6 x + 9 = 0$ by factoring.

A) $x = 3 , x = - 3$
B) x=3
C) x=-3
D) $x = 0 , x = 3$
E) $x = 3 , x = \frac { 3 } { 2 }$

Answer 3

x=3

Question 4

Solve the equation of quadratic form. $x - 4 \sqrt { x } - 12 = 0$

A) $x = - 4 ; x = 36$
B) $x = - 2 ; x = 6$
C) x=36
D) $x = 2 ; x = - 6$
E) $x = \sqrt { 2 } i ; x = \sqrt { 6 }$

Question 5

Solve the equation $( 4 m - 5 ) ^ { 2 } - 200 = 0$ by using the Square Root Property.

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

Question 6

Solve $x ^ { 2 } + 2 x + 1 \geq 0$ by the Square Root Property, if possible.

A) $u ^ { 2 } - 144 = 0$
B) $u = 12$
C) $u = 0 , u = - 12$
D) $u = 24$
E)no solutions

Question 7

Find all real and complex solutions of the quadratic equation $x ^ { 2 } + 256 = 0$ .

A) -256
B) $\pm 256 i$
C) $\pm 16$
D) $\pm 16 i$
E) $16 i$

Question 8

Solve the equation $( x - 5 ) ^ { 2 } = - 8$ by using the Square Root Property.

A) $5 \pm \sqrt { 2 } i$
B) $5 \pm 2 \sqrt { 2 }$
C) - $5 \pm \sqrt { 2 } i$
D) - $5 \pm 2 \sqrt { 2 }$
E) $5 \pm 2 \sqrt { 2 } i$

Question 9

Solve $t ^ { 2 } + 7 t = 0$ by factoring.

A) $t = 0 , t = 7$
B) t=0
C) $t = 0 , t = - 7$
D) $t = 0 , t = \frac { 7 } { 2 }$
E) t=-7

Question 10

Solve $25 ( y + 5 ) ^ { 2 } = 81$ by the Square Root Property, if possible.

A) $y = - \frac { 16 } { 5 } , y = - \frac { 34 } { 5 }$
B) $y = - \frac { 16 } { 5 } , y = \frac { 34 } { 5 }$
C) $y = 4 , y = - 14$
D) $y = \frac { 9 } { 5 } , y = - \frac { 9 } { 5 }$
E)no solutions

Question 11

Find all real and complex solutions of the quadratic equation $6 x ^ { 2 } - 5 x = 0$ .

A) $0,\frac { 5 } { 6 }$
B) $0 , \frac { 5 } { 6 } i$
C) $\frac { 36 } { 5 }$
D) $\frac { 5 } { 6 } i$
E) $0 , \frac { 6 } { 5 }$

Question 12

Solve $u ( u - 10 ) - 6 ( u - 10 ) = 0$ by factoring.

A) $u = 6 , u = 10$
B) $u = 0 , u = \frac { 3 } { 5 }$
C) $u = - 6 , u = - 10$
D) $u = 0 , u = 10$
E) $u = 6 , u = - 10$

Question 13

Solve the equation by using the Square Root Property. $9 u ^ { 2 } + 30 = 0$

A) $u = \pm \sqrt { 30 }$
B) $u = \pm \frac { \sqrt { 30 } } { 9 } i$
C) $u = \pm \frac { \sqrt { 30 } } { 3 }$
D) $u = \pm \frac { \sqrt { 30 } } { 9 }$
E) $u = \pm \frac { \sqrt { 30 } } { 3 } i$

Question 14

Solve the equation $\left( x ^ { 2 } - 13 \right) ^ { 2 } + 3 \left( x ^ { 2 } - 13 \right) - 4 = 0$ . (Find all real and complex solutions.)

A) $\pm 3 , \pm \sqrt { 14 } i$
B) $\pm 13 , \pm \sqrt { 14 } i$
C) $\pm 3 , \pm \sqrt { 14 }$
D) $\pm 13 , \pm 14 i$
E) $\pm 9 , \pm 14$

Question 15

Solve $( y - 5 ) ^ { 2 } = 144$ by the Square Root Property, if possible.

A) $y = 12 , y = - 12$
B) $y = 17 , y = - 7$
C) y=139
D) $y = - 17 , y = - 7$
E)no solutions

Question 16

Solve the equation $8 ( 6 - x ) - 3 x ( 6 - x ) = 0$ by factoring.

A) $\frac { 8 } { 3 } , 6$
B) $- \frac { 8 } { 3 } , - 6$
C) $\frac { 8 } { 3 } , 48$
D) $\frac { 3 } { 8 } , 6$
E) $- \frac { 3 } { 8 } , - 48$

Question 17

Find all real and complex solutions of the quadratic equation $( x + 7 ) ^ { 2 } + 28 = 0$ .

A) $4 \pm 7 \sqrt { 7 }$
B) $7 \pm 2 \sqrt { 7 }$
C) $7 \pm 4 \sqrt { 7 } i$
D) $- 2 \pm 7 \sqrt { 7 } i$
E) $- 7 \pm 2 \sqrt { 7 } i$

Question 18

Solve the equation $x ^ { 4 } - 37 x ^ { 2 } + 36 = 0$ . (Find all real and complex solutions.)

A) $\pm 1 , \pm 6 i$
B) $\pm 36$
C) $\pm 1 , \pm 36$
D) $\pm 1 , \pm 6$
E) $\pm 6 i$

Question 19

Solve the equation by using the Square Root Property. $( 2 x + 2 ) ^ { 2 } = - 17$

A) $x = \pm \sqrt { \frac { 19 } { 2 } } i$
B) $x = \frac { - 2 \pm \sqrt { 17 } i } { 2 }$
C) $x = \pm \frac { \sqrt { 17 } i } { 2 } - 2$
D) $x = \frac { \pm 2 + \sqrt { 17 } i } { 2 }$
E) $x = 2 \pm \sqrt { 17 } i$

Question 20

Solve $h ^ { 2 } = 100$ by the Square Root Property, if possible.

A) $h = 10 , h = - 10$
B) h=20
C) h=10
D) $h = 0 , h = 10$
E)no solutions

Question 21

Find the real solutions of the equation $\sqrt { 2 x + 114 } = x - 5$ .

A) $6 - \sqrt { 5 }$
B) $6 \pm 5 \sqrt { 5 }$
C) $12 \pm 10 \sqrt { 5 }$
D) $5 + 6 \sqrt { 5 }$
E) $10 + \sqrt { 5 }$

Question 22

What term should be added to $y ^ { 2 } - 14 y$ to make it a perfect square trinomial?

A) 196
B) 49
C)1
D) 7
E) 14

Question 23

What term should be added to $y ^ { 2 } - \frac { 1 } { 5 } y$ to make it a perfect square trinomial?

A) 5
B) $\frac { 1 } { 100 }$
C) 100
D) $\frac{5}{2}$
E) $\frac { 1 } { 50 }$

Question 24

Solve $u ^ { 2 } - 16 u = 0$ by completing the square.

A) $u = - 16$
B) $u = 0 , u = - 16$
C) $u = 0 , u = 16$
D) $u = 1 , u = 16$
E) $u = 80 , u = - 48$

Question 25

What term should be added to $t ^ { 2 } + 11 t$ to make it a perfect square trinomial?

A) $\frac { 4 } { 121 }$
B) $\frac { 121 } { 4 }$
C) $\frac { 11 } { 4 }$
D) 121
E) 11

Question 26

Solve the equation $x ^ { 1 / 3 } - 2 x ^ { 1 / 6 } - 24 = 0$ . (Find all real and complex solutions.)

A) $46,656$
B) $- 46,656 ; 4,096$
C) $46,656 ; 4,096$
D) $4,096$
E) $46,656 ; - 4,096$

Question 27

The height h (in feet)of an object dropped from a tower 54 feet high is modeled by $h = 54 - 16 t ^ { 2 }$ , where t is the time in seconds. How long does it take for the object to reach the ground? Round your answer to two decimal places.

A)3.86 seconds
B)3.67 seconds
C)0.46 second
D)1.84 seconds
E)6.16 seconds

Question 28

Solve the equation by completing the square. $y ^ { 2 } + 5 y + 12 = 0$

A) $y = - \frac { 5 } { 2 } \pm$ $2 \sqrt { 3 }$
B) $y = \frac { 5 } { 2 } \pm \frac { \sqrt { 23 } i } { 2 }$
C) $y = - \frac { 5 } { 2 } \pm \frac { \sqrt { 23 } i } { 2 }$
D) $y = \frac { 5 } { 2 } \pm \frac { \sqrt { 38 } i } { 2 }$
E) $y = - \frac { 5 } { 2 } \pm \frac { \sqrt { 38 } i } { 2 }$

Question 29

Solve $\frac { x } { 3 } + \frac { 2 } { x } = 6$ . Round your answer to two decimal places.

A) $x = - 17.66 , x = - 0.34$
B) $x = 6.00 , x = 3.00$
C) $x = - 17.66 , x = 0.71$
D) $x = 17.66 , x = 0.34$
E) $x = - 0.34 , x = 0.71$

Question 30

Solve $5 z ^ { 2 } - 5 z - 4 = 0$ by completing the square. Round your answer to two decimal places.

A) $x = - 1.52 , x = 0.52$
B) $x = 1.12 , x = 0.52$
C) $x = - 1.52 , x = 1.12$
D) $x = 1.52 , x = - 0.52$
E) $x = 5 , x = 4$

Question 31

Solve the equation by completing the square. Round your solution to two decimal places. $0.1 x ^ { 2 } + 0.5 x = 0.7$

A) $x = 6.14 , x = - 1.14$
B) $x = - 5.58 , x = 0.58$
C) $x = 1.14 , x = - 6.14$
D) $x = - 0.13 \pm 3 i$
E) $x = 0.13 \pm 3 i$

Question 32

After two years, a $1000 investment, compounded annually at interest rate r , will yield an amount of $1000 ( 1 + r ) ^ { 2 }$ . If the amount after two years is $1166.40, find the rate r . Round your answer to three decimal places.

A) $r = 2.080$
B) $r = 0.080$
C) $r = 0.166$
D) $r = 1.080$
E) $r = 1.166$

Question 33

Solve the equation of quadratic form. $\frac { 1 } { x ^ { 2 } } - \frac { 3 } { x } - 18 = 0$

A) $x = \frac { 1 } { 3 } ; x = - \frac { 1 } { 6 }$
B) $x = - \frac { 1 } { 3 } ; x = \frac { 1 } { 6 }$
C) $x = 3 ; x = - 6$
D) $x = 9 ; x = 36$
E) $x = - 3 ; x = 6$

Question 34

Solve $x ^ { 2 } - 8 x - 9 = 0$ by completing the square, if possible.

A) $x = - 1 , x = 9$
B) $x = 8 , x = - 9$
C) $x = 1 , x = - 9$
D) $x = - 8 , x = - 9$
E)no solutions

Question 35

Solve the equation $x ^ { 2 } - 4 x - 3 = 0$ by completing the square. Give the solutions in exact form and in decimal form rounded to two decimal places. (The solutions may be complex numbers.)

A) $4 + \sqrt { 7 } i \approx 4 + 2.65 i$ ; $4 - \sqrt { 7 } i \approx 4 - 2.65 i$
B) $2 + \sqrt { 7 } i \approx 2 + 2.65 i$ ; $2 - \sqrt { 7 } i \approx 2 - 2.65 i$
C) $4 + \sqrt { 7 } \approx 6.65$ ; $4 - \sqrt { 7 } \approx 1.35$
D) $2 + \sqrt { 7 } \approx 4.65$ ; $2 - \sqrt { 7 } \approx - 0.65$
E) $- 2 + \sqrt { 7 } \approx 0.65$ ; $- 2 - \sqrt { 7 } \approx - 4.65$

Question 36

Use a graphing calculator to approximate the x -intercepts of the graph of the function $y = x ^ { 2 } + 2 x - 5$ . Round your answer to two decimal places wherever applicable.

A) $( 5,0 ) , ( - 5,0 )$
B) $( 0,3.45 ) , ( 0 , - 1.45 )$
C) $( 0,1.45 ) , ( 0 , - 3.45 )$
D) $( 1.45,0 ) , ( - 3.45,0 )$
E) $( 3.45,0 ) , ( - 1.45,0 )$

Question 37

Solve the equation $x \left( x - \frac { 2 } { 3 } \right) = 14$ by completing the square. Give the solutions in exact form and in decimal form rounded to two decimal places. (The solutions may be complex numbers.)

A) $- \frac { 1 } { 3 } + \frac { \sqrt { 127 } } { 6 } \approx 1.54 ; - \frac { 1 } { 3 } - \frac { \sqrt { 127 } } { 6 } \approx - 2.21$
B) $\frac { 2 } { 3 } + \frac { \sqrt { 127 } } { 3 } \approx 4.42 ; \frac { 2 } { 3 } - \frac { \sqrt { 127 } } { 3 } \approx - 3.09$
C) $\frac { 1 } { 3 } + \frac { \sqrt { 127 } } { 3 } \approx 4.09 ; \frac { 1 } { 3 } - \frac { \sqrt { 127 } } { 3 } \approx - 3.42$
D) $\frac { 2 } { 3 } + \frac { \sqrt { 127 } } { 6 } \approx 2.54 ; \frac { 2 } { 3 } - \frac { \sqrt { 127 } } { 6 } \approx - 1.21$
E) $- \frac { 1 } { 3 } + \frac { \sqrt { 127 } } { 3 } \approx 3.42 ; - \frac { 2 } { 3 } - \frac { \sqrt { 127 } } { 3 } \approx - 4.42$

Question 38

Solve the equation by completing the square. $4 x ^ { 2 } - 5 x + 28 = 0$

A) $x = \frac { 5 } { 8 } \pm \frac { \sqrt { 423 } i } { 8 }$
B) $x = \frac { 25 } { 8 } \pm \frac { \sqrt { 62 } i } { 2 }$
C) $x = \frac { 5 } { 8 } \pm \frac { \sqrt { 473 } } { 8 }$
D) $x = \frac { 5 } { 8 } \pm \frac { \sqrt { 62 } } { 8 }$
E) $x = \frac { 25 } { 8 } \pm \frac { \sqrt { 423 } } { 4 }$

Question 39

Solve the equation $x ^ { 2 / 3 } - 2 x ^ { 1 / 3 } - 63 = 0$ . (Find all real and complex solutions.)

A) 729
B) $343,729$
C) $- 343 i , 729 i$
D) $7 i , 9 i$
E) $- 7,9$

Question 40

Solve $u ^ { 2 } - 7 u - 4 = 0$ by completing the square, if possible.

A) $y = \frac { \sqrt { 65 } } { 2 } , y = - \frac { \sqrt { 65 } } { 2 }$
B) $y = \frac { 7 } { 2 } + \frac { \sqrt { 65 } } { 2 } , y = \frac { 7 } { 2 } - \frac { \sqrt { 65 } } { 2 }$
C) $y = 7 + \frac { \sqrt { 65 } } { 2 } , y = 7 - \frac { \sqrt { 65 } } { 2 }$
D) $y = - \frac { 7 } { 2 } + \frac { \sqrt { 65 } } { 2 } , y = - \frac { 7 } { 2 } - \frac { \sqrt { 65 } } { 2 }$
E)no solutions

Question 41

Solve the quadratic equation. $x ^ { 2 } + 6 x + 25 = 0$

A) $x = 14 , x = - 2$
B) $x = 1 , x = - 7$
C) $x = - 6 \pm 8 i$
D) $x = 6 \pm 8 i$
E) $x = - 3 \pm 4 i$

Question 42

Solve the equation by using the Quadratic Formula. $u ^ { 2 } - 10 u + 18 = 0$

A) $u = 10 \pm$ $\sqrt { 7 }$
B) $u = 10 \pm$ $\sqrt { 43 }$
C) $u = 5 \pm$ $\sqrt { 7 }$
D) $u = - 10 \pm$ $\sqrt { 43 }$
E) $u = - 5 \pm$ $\sqrt { 7 }$

Question 43

Use the Quadratic Formula to solve $t ^ { 2 } + 5 t + 6 = 0$ .

A) $t = 2 , t = 3$
B) $t = - 2 , t = 3$
C) $t = 2 , t = - 3$
D) $t = - 2 , t = - 3$
E)no solutions

Question 44

Write $x ^ { 2 } + 6 x = - 5$ in general form.

A) $x ^ { 2 } + 11 x + 5 = 0$
B) $x ^ { 2 } + 6 x + 5 = 0$
C) $x ^ { 2 } + 6 x - 5 = 0$
D) $x ^ { 2 } - 6 x + 5 = 0$
E) $x ^ { 2 } = - 6 x - 5$

Question 45

Determine all real values of x for which the function $7 x ^ { 2 } - 13 x + 1$ has the value 3.

A) $- \frac { 13 } { 7 } \pm \frac { 13 \sqrt { 57 } } { 14 }$
B) $\frac { 13 } { 14 } \pm \frac { \sqrt { 57 } } { 14 }$
C) $\frac { 13 } { 7 } \pm \frac { 13 \sqrt { 57 } } { 7 }$
D) $\frac { 13 } { 7 } \pm \frac { \sqrt { 57 } } { 14 }$
E) $- \frac { 13 } { 14 } \pm \frac { \sqrt { 57 } } { 7 }$

Question 46

Write the quadratic equation having solutions $- 4 + \sqrt { 5 } , - 4 - \sqrt { 5 }$

A) $x ^ { 2 } - 8 x + 11 = 0$
B) $x ^ { 2 } + 8 x + 11 = 0$
C) $x ^ { 2 } + 4 x - 21 = 0$
D) $x ^ { 2 } - 4 x - 9 = 0$
E) $x ^ { 2 } + 8 x + 9 = 0$

Question 47

Solve the equation by using the Quadratic Formula. $x ^ { 2 } - 8 x + 28 = 0$

A) $x = - 32 \pm$ $2 i \sqrt { 3 }$
B) $x = - 4 \pm$ $2 i \sqrt { 3 }$
C) $x = - \frac { 4 } { 2 } \pm$ $2 i \sqrt { 3 }$
D) $x = - \frac { 4 } { 2 } \pm$ $2 i \sqrt { 3 }$ .
E) $x = 4 \pm$ $2 i \sqrt { 3 }$

Question 48

Use a graphing calculator to determine the number of real solutions of the quadratic equation $7 x ^ { 2 } - 6 x - 6 = 0$ .

A)one real solution
B)no real solutions
C)two real solutions

Question 49

Use the Quadratic Formula to solve $12 x ^ { 2 } - 12 x + 3 = 0$ .

A) $x = \frac { 1 } { 2 }$
B) $x = \frac { 1 } { 2 } \pm 12 \sqrt { 2 }$
C) $x = 12 \sqrt { 2 }$
D) $x = - \frac { 1 } { 2 }$
E)no solutions

Question 50

You have 200 meters of fencing to enclose two adjacent rectangular corrals. The total area of the enclosed region is 1000 square meters. What are the dimensions of each corral? (The corrals are the same size.)

A) $\frac { 5 \sqrt { 1375 } } { 2 }$ +25 meters by $\frac { 100 + 10 \sqrt { 1375 } } { 3 }$ maters
B) $\frac { 5 \sqrt { 1375 } } { 2 }$ +25 meters by $\frac { 100 - 10 \sqrt { 40 } } { 3 }$ maters
C) $\frac { 5 \sqrt { 1375 } } { 2 }$ +25 meters by $\frac { 100 + 10 \sqrt { 40 } } { 3 }$ maters
D) $\frac { 5 \sqrt { 40 } } { 2 }$ +25 meters by $\frac { 100 - 10 \sqrt { 40 } } { 3 }$ maters
E) $\frac { 5 \sqrt { 40 } } { 2 }$ +25 meters by $100 - \frac { 5 \sqrt { 40 } } { 2 }$ maters

Question 51

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

A)two real solutions
B)one real solution
C)no real solutions

Question 52

Use the Quadratic Formula to solve $0.09 s ^ { 2 } - 0.12 s + 0.04 = 0$ . Round your answer(s)to two decimal places.

A) $s = 0.67$
B) $s = 0.67 , s = - 0.67$
C) $s = 0.89$
D) $s = 0.78 , s = 2.00$
E)no solutions

Question 53

An open box with a rectangular base of x inches by x+4 inches has a height of 6 inches. The volume of the box is 702 cubic inches. Find the dimensions of the box.

A) 11 inches by 15 inches by 6 inches
B) 9 inches by 13 inches by 6 inches
C) 15 inches by 19 inches by 6 inches
D) 13 inches by $17$ inches by 6 inches
E) $13$ inches by $15$ inches by 6 inches

Question 54

Use the discriminant to determine the number of real solutions of $18 x ^ { 2 } - 12 x + 2 = 0$ .

A)no real solutions
B)two real solutions
C)one real solution

Question 55

Use the Quadratic Formula to solve $4 x ^ { 2 } - 12 x + 6 = 0$ , if possible. Round your answer(s)to two decimal places.

A) $x = 18.87 , x = 17.13$
B) $x = - 0.63 , x = - 2.37$
C) $x = 9.46 , x = 2.54$
D) $x = 2.37 , x = 0.63$
E)no solutions

Question 56

Write $x ( 4 - x ) = 14$ in general form.

A) $x ^ { 2 } + 4 x - 14 = 0$
B) $x ^ { 2 } - 4 x + 14 = 0$
C) $( 4 - x ) = \frac { 14 } { x ^ { 2 } }$
D) $3 x - 14 = 0$
E) $x ^ { 2 } + 4 x + 14 = 0$

Question 57

The revenue R (in dollars)for selling x units of an infant stroller is modelled by $R = x \left( 50 - \frac { 1 } { 4 } x \right) , 0 < x < 100$ . Find the number of strollers that must be sold to produce a revenue of $2176 . Round your answer to the nearest integer.

A) 26 strollers
B) 64 strollers
C) 45 strollers
D) 32 strollers
E) $43$ strollers

Question 58

Write the quadratic equation having solutions $4 i , - 4 i$

A) $x ^ { 2 } - 4 = 0$
B) $x ^ { 2 } - 16 = 0$
C) $x ^ { 2 } + 4 = 0$
D) $x ^ { 2 } + 16 = 0$
E) $x ^ { 2 } + 4 x + 16 = 0$

Question 59

Solve $2 y ( y - 16 ) + 5 ( y - 16 ) = 0$ .

A) $y = 16 , y = - 5$
B) $y = - 16 , y = \frac { 2 } { 5 }$
C) $y = 16 , y = - \frac { 5 } { 2 }$
D) $y = 16 , y = - \frac { 2 } { 5 }$
E) $y = - 16 , y = - \frac { 5 } { 2 }$

Question 60

Use a graphing calculator to determine the number of real solutions of the quadratic equation $4 x ^ { 2 } - 3 x + 9 = 0$ .

A)one real solution
B)no real solutions
C)two real solutions

Question 61

Find the vertex of $y = 6 x ^ { 2 } + 12 x - 6$ .

A) $( - 1 , - 12 )$
B) $( 1,12 )$
C) $( 0 , - 12 )$
D) $( - 2,42 )$
E) $( - 1,12 )$

Question 62

Graph $y = - \left( x ^ { 2 } - 2 x - 6 \right)$ .

A)
B)
C)
D)
E)

Question 63

Find the vertex of the graph of the function $y = 9 x ^ { 2 } + 6 x + 4$ by using the formula $x = - b / ( 2 a )$ .

A) $( 24,5,332 )$
B) $\left( - \frac { 1 } { 3 } , 3 \right)$
C) $\left( \frac { 1 } { 3 } , 7 \right)$
D) $( - 24,5,044 )$
E) $\left( - \frac { 1 } { 3 } , 7 \right)$

Question 64

Determine if the parabola $y = x ^ { 2 } - 5 x + 8$ opens upward or downward.

A)parabola opens downward
B)parabola opens upward

Question 65

Graph $y = - \frac { 1 } { 2 } x ^ { 2 } + 2 x - 2$ .

A)
B)
C)
D)
E)

Question 66

Write an equation of the parabola $y = a ( x - h ) ^ { 2 } + k$ that satisfies the conditions. Vertex: (2,6) ; a=1

A) $y = ( x + 2 ) ^ { 2 } + 6$
B) $y = ( x + 6 ) ^ { 2 } + 2$
C) $y = ( x - 6 ) ^ { 2 } + 2$
D) $y = ( x - 2 ) ^ { 2 } + 6$
E) $y = ( x + 2 ) ^ { 2 } - 6$

Question 67

Match the equation $y = ( x + 1 ) ^ { 2 } + 3$ with its graph.

A)
B)
C)
D)
E)

Question 68

Find the intercepts of $y = 9 x ^ { 2 } - 8 x + 8$ .

A)x -intercept: $\left( - \frac { 4 } { 9 } , 0 \right)$ y -intercepts: (0,8)
B)no x -intercepts y -intercept: (0,8)
C)x -intercept: (8,0) no y -intercepts
D)no x -intercepts y -intercept: (0,-8)
E)x -intercept: (8,0) y -intercept: (0,8)

Question 69

Graph $y = x ^ { 2 } - 3 x$ .

A)
B)
C)
D)
E)

Question 70

Write the equation of the parabola in standard form and find the vertex of its graph. $y = x ^ { 2 } + 10 x + 16$

A) $y = ( x + 5 ) ^ { 2 } - 9$ ; vertex: $( 5 , - 41 )$
B) $y = ( x - 5 ) ^ { 2 } + 11$ ; vertex: $( 5,41 )$
C) $y = ( x + 8 ) ( x + 2 )$ ; vertex: $( 10,16 )$
D) $y = ( x + 5 ) ^ { 2 } - 9$ ; vertex: $( - 5 , - 9 )$
E) $y = ( x + 5 ) ^ { 2 } + 41$ ; vertex: $( - 5,41 )$

Question 71

From the roof of a building 125 feet above the ground, you toss a coin upward with an initial velocity of 11 feet per second. The height h (in feet)of the coin at time t (in seconds)after it is tossed is modeled by $h = - 16 t ^ { 2 } + 11 t + 125$ . Find the time when the coin hits the ground. Round your answer to two decimal places

A)2.47 seconds
B)50.56 seconds
C)3.16 seconds
D)39.56 seconds
E)6.51 seconds

Question 72

Sketch the parabola given by $y = - 2 x ^ { 2 } - 12 x - 21$ and then identify its vertex.

A)vertex: (-2,-2)
B)vertex: (3,4)
C)vertex: (-2,-3)

D)vertex: (2,4)
E)vertex: (-3,-3)

Question 73

Find the intercepts of $y = 2 x - x ^ { 2 }$ .

A)x -intercept: (0,0) y -intercepts: (0,0) and (2,0)
B)x -intercepts: (0,0) and (2,0) y -intercept: (0,0)
C)x -intercepts: (0,0) and $\left( \frac { 1 } { 2 } , 0 \right)$ y -intercept: (0,0)
D)x -intercepts: (0,0) and $( - 2,0 )$ y -intercept: $( 0,0 )$
E)x -intercepts: $( - 2,0 )$ and $( 2,0 )$ y -intercept: $( 0,0 )$

Question 74

Determine if the parabola $y = - 2 x ^ { 2 } - 7 x + 8$ opens upward or downward.

A)parabola opens upward
B)parabola opens downward

Question 75

Use the transformations of the graph of $f ( x ) = x ^ { 2 }$ to sketch the graph of $h ( x ) = - ( x - 2 ) ^ { 2 } - 3$ .

A)
B)
C)
D)
E)

Question 76

Identify the transformations of the graph of $f ( x ) = x ^ { 2 }$ that would produce the graph of $h ( x ) = - ( x + 3 ) ^ { 2 } + 4$ .

A)horizontal shift 3 units left; vertical shift 4 units upward
B)horizontal shift 3 units right; reflection in the x -axis; vertical shift 4 units downward
C)horizontal shift 4 units right; vertical shift 3 units downward
D)horizontal shift 4 units left; reflection in the x -axis; vertical shift 3 units upward
E)horizontal shift 3 units left; reflection in the x -axis; vertical shift 4 units upward

Question 77

From the roof of a building 100 feet above the ground, you toss a coin upward with an initial velocity of 6 feet per second. The height h (in feet)of the coin at time t (in seconds)after it is tossed is modeled by $h = - 16 t ^ { 2 } + 6 t + 100$ . Find the time when the coin is again 100 feet above the ground.

A) $\frac { 3 } { 8 }$ second
B)0 second
C) $\frac { 3 } { 16 }$ second
D) $\frac { 3 } { 4 }$ second
E) $\frac { 8 } { 3 }$ seconds

Question 78

Find the vertex of $y = 5 - 3 x - x ^ { 2 }$ .

A) $\left( - \frac { 3 } { 2 } , \frac { 4 } { 29 } \right)$
B) $\left( \frac { 2 } { 3 } , \frac { 4 } { 29 } \right)$
C) $\left( - \frac { 3 } { 2 } , \frac { 29 } { 4 } \right)$
D) $\left( \frac { 3 } { 2 } , \frac { 29 } { 4 } \right)$
E) $\left( - 3 , \frac { 29 } { 4 } \right)$

Question 79

Sketch the graph of $h ( x ) = - ( x + 4 ) ^ { 2 }$ .

A)
B)
C)
D)
E)

Question 80

Use the Quadratic Formula to solve $\sqrt { 9 x + 5 } = x - 1$ , if possible. Round your answer(s)to two decimal places.

A) $x = 22.70 , x = - 0.70$
B) $x = - 11.35 , x = - 0.35$
C) $x = 0.35 , x = - 6.62$
D) $x = 11.35$
E)no solutions