Deck 3: Quadratic, Piecewise-Defined, and Power Functions

Question 1

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

A) Concave down
B) Concave up

Answer 1

A

Question 2

Determine if the vertex of the graph is a maximum point or a minimum point.
$y = ( x + 1 ) ^ { 2 }$

A) Minimum
B) Maximum

Answer 2

A

Question 3

Determine if the vertex of the graph is a maximum point or a minimum point.
$y = - \frac { 2 } { 5 } ( x + 3 ) ^ { 2 } - 1$

A) Maximum
B) Minimum

Answer 3

A

Question 4

Determine if the vertex of the graph is a maximum point or a minimum point.
$y = - ( x + 2 ) ^ { 2 } - 4$

A) Maximum
B) Minimum

Question 5

$f ( x ) = - 3 x ^ { 2 } - 3 x - 9$

A) Concave up
B) Concave down

Question 6

Determine if the vertex of the graph is a maximum point or a minimum point.
$y = - ( x + 1 ) ^ { 2 }$

A) Minimum
B) Maximum

Question 7

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

A) Concave up
B) Concave down

Question 8

Determine if the vertex of the graph is a maximum point or a minimum point.
$y = x ^ { 2 } - 2 x + 1$

A) Minimum
B) Maximum

Question 9

$y = - ( x + 5 ) ^ { 2 } - 3$

A) Concave up
B) Concave down

Question 10

Determine if the vertex of the graph is a maximum point or a minimum point.
$y = - x ^ { 2 } + 4$

A) Minimum
B) Maximum

Question 11

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

A) Concave down
B) Concave up

Question 12

Determine if the vertex of the graph is a maximum point or a minimum point.
$g ( x ) = ( x - 1 ) ^ { 2 } + 5$

A) Minimum
B) Maximum

Question 13

Determine if the vertex of the graph is a maximum point or a minimum point.
$f ( x ) = 3 x ^ { 2 } + 2 x + 2$

A) Minimum
B) Maximum

Question 14

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

A) Concave up
B) Concave down

Question 15

Determine if the vertex of the graph is a maximum point or a minimum point.
$y = 4 ( x + 2 ) ^ { 2 } + 3$

A) Minimum
B) Maximum

Question 16

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

A) Concave up
B) Concave down

Question 17

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

A) Concave up
B) Concave down

Question 18

Determine if the vertex of the graph is a maximum point or a minimum point.
$f ( x ) = - 2 x ^ { 2 } - 2 x + 2$

A) Maximum
B) Minimum

Question 19

$y = 4 ( x + 1 ) ^ { 2 } + 2$

A) Concave up
B) Concave down

Question 20

$y = - \frac { 2 } { 5 } ( x + 5 ) ^ { 2 } - 4$

A) Concave down
B) Concave up

Question 21

Give the coordinates of the vertex and graph the equation in a window that includes the vertex.
$y=x^{2}-2 x-8$

A) Vertex: $( - 1 , - 7 )$

B) Vertex: $( - 1 , - 9 )$

C) Vertex: $( 1 , - 9 )$

D) Vertex: $( 1,7 )$

Question 22

Graph the quadratic equation on [ $[ - 10,10 ] \text { by } [ - 10,10 ]$ oes this window give a complete graph?

- $f(x)=-0.08 x^{2}+2 x-4$

A)

B)


C)
$\text { No }$


D)
$\text { Yes }$


Yes No

Question 23

Sketch the complete graph of the function.

- $y=8 x^{2}-32 x+38$

A)

B)

C)

D)

Question 24

Graph the quadratic equation on [ $[ - 10,10 ] \text { by } [ - 10,10 ]$ oes this window give a complete graph?

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

A)

B)


C)
$\text { Yes }$


D)
$\text { Yes }$


No No

Question 25

Give the coordinates of the vertex and graph the equation in a window that includes the vertex.

- $y=2 x^{2}-60 x+16$

A) Vertex: $( 15 , - 434 )$

B) Vertex: $( - 15 , - 434 )$

C) Vertex: $( 30 , - 884 )$

D) Vertex: $( 15 , - 390 )$

Question 26

Graph the quadratic equation on [ $[ - 10,10 ] \text { by } [ - 10,10 ]$ oes this window give a complete graph?

- $f(x)=0.1 x^{2}-2 x-6$

A)

B)


C)
$\text { No }$


D)
$\text { No }$



No Yes

Question 27

Graph the quadratic equation on [ $[ - 10,10 ] \text { by } [ - 10,10 ]$ oes this window give a complete graph?

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

A)

B)

C)
$\text { Yes }$


D)
$\text { No }$


Yes Yes

Question 28

Provide an appropriate response.
If the points in the table lie on a parabola, write the equation whose graph is the parabola. $\begin{array}{c|c|c|c|c|c|c}\mathrm{x} & 5 & 4 & 3 & 2 & 1 & 0 \\\hline \mathrm{y} & -24 & -9 & 0 & 3 & 0 & -9\end{array}$

A) $y = - 3 x ^ { 2 } + 12 x - 9$
B) $y = - 3 ( x + 2 ) ^ { 2 } + 3$
C) $y = - 3 ( x + 2 ) ^ { 2 } - 3$
D) $y = 3 x ^ { 2 } + 12 x - 9$

Question 29

Give the coordinates of the vertex and graph the equation in a window that includes the vertex.
$$y = - x ^ { 2 } - 4 x - 3$$

A) Vertex: $( - 0.5,3.25 )$

B) Vertex: $( - 2 , - 1 )$

C) Vertex: $( - 2,1 )$

D) Vertex: $( 2,1 )$

Question 30

Graph the quadratic equation on [ $[ - 10,10 ] \text { by } [ - 10,10 ]$ oes this window give a complete graph?

- $f(x)=-4 x^{2}+2 x-1$

A)

B)


C)
$\mathrm { No }$


D)
$\mathrm { No }$


Yes Yes

Question 31

Give the coordinates of the vertex and graph the equation in a window that includes the vertex.

- $y=2 x^{2}-12 x+22$

A) Vertex: $( 4,3 )$

B) Vertex: $( - 3 , - 4 )$

C) Vertex: $( - 4 , - 3 )$

D) Vertex: $( 3,4 )$

Question 32

Give the coordinates of the vertex and graph the equation in a window that includes the vertex.
$y=(x-4)^{2}+2$

A) Vertex: $( 4 , - 2 )$

B) Vertex: $( 4,2 )$

C) Vertex: $( - 4,2 )$

D) Vertex: $( - 4 , - 2 )$

Question 33

Give the coordinates of the vertex and graph the equation in a window that includes the vertex.

- $y=(x-17)^{2}+8$

A) Vertex: $( - 17,8 )$

B) Vertex: $( 8,17 )$

C) Vertex: $( 17,8 )$

D) Vertex: $( 8 , - 17 )$

Question 34

Provide an appropriate response.
Write the equation of the quadratic function whose graph is shown.

A) $y = ( x - 1 ) ^ { 2 } - 5$
B) $y = ( x + 1 ) ^ { 2 } - 5$
C) $y = - ( x - 1 ) ^ { 2 } + 5$
D) $y = - ( x - 1 ) ^ { 2 } - 5$

Question 35

Give the coordinates of the vertex and graph the equation in a window that includes the vertex.
$y=(x+4)^{2}$

A) Vertex: $( 4,0 )$

B) Vertex: $( 0,4 )$

C) Vertex: $( - 4,0 )$


D) Vertex: $( 0 , - 4 )$

Question 36

Sketch the complete graph of the function.
$$f ( x ) = x ^ { 2 } + 200 x - 600$$

A)

B)

C)

D)

Question 37

Provide an appropriate response.
If the points in the table lie on a parabola, write the equation whose graph is the parabola. $\begin{array}{c|c|c|c|c}\mathrm{x} & -3 & -2 & -1 & 0 \\\hline \mathrm{y} & -1 & -4 & -1 & 8\end{array}$

A) $y = 3 x ^ { 2 } + 12 x + 8$
B) $y = 3 x ^ { 2 } + 12 x - 8$
C) $y = 3 ( x + 2 ) ^ { 2 } + 4$
D) $y = 3 ( x - 2 ) ^ { 2 } + 4$

Question 38

Give the coordinates of the vertex and graph the equation in a window that includes the vertex.
$$y = x ^ { 2 } + 5$$

A) Vertex: $( 0,5 )$

B) Vertex: $( 0 , - 5 )$

C) Vertex: $( - 5,0 )$

D) Vertex: $( 5,0 )$

Question 39

Provide an appropriate response.
Write the equation of the quadratic function whose graph is shown. A) $y = - ( x + 4 ) ^ { 2 } + 6$
B) $y = - ( x - 4 ) ^ { 2 } + 6$
C) $y = - 2 ( x - 4 ) ^ { 2 } + 6$
D) $y = ( x - 4 ) ^ { 2 } + 6$

Question 40

Give the coordinates of the vertex and graph the equation in a window that includes the vertex.

- $y=-0.2 x^{2}-14 x+6$

A) Vertex: $( - 35,251 )$

B) Vertex: $( - 17.5,67.25 )$

C) Vertex: $( 35,251 )$

D) Vertex: $( 17.5,67.25 )$

Question 41

Use the graph of the function to estimate the x-intercepts.
$g(x)=-2 x^{2}-3 x+5$

A) $x = - 5 , x = 2$
B) $x = - 3 , x = 5$
C) $x = - 2.5 , x = 1$
D) $x = - 1 , x = 2.5$

Question 42

Given the following revenue and cost functions, find the x-value that makes profit a maximum. (Recall that profit equals revenue minus cost.) $$R ( x ) = 58 x - 2 x ^ { 2 } ; C ( x ) = 25 x + 98$$

A) 9.25
B) 14.5
C) 16.5
D) 8.25

Question 43

Use the graph of the function to estimate the x-intercepts.
$f(x)=4 x^{2}-20 x+21$

A) $x = - 29 , x = 21$
B) $x = - 3.5 , x = - 1.5$
C) $x = 1.5 , x = 3.5$
D) $x = 6 , x = 14$

Question 44

Use the graph of the function to estimate the x-intercepts.
$f(x)=-x^{2}+4 x+5$

A) $x = 4 , x = 5$
B) $x = - 5 , x = - 1$
C) $x = - 1 , x = 5$
D) $x = - 5 , x = 1$

Question 45

Use the graph of the function to estimate the x-intercepts.
$g(x)=-8 x^{2}+18 x+5$

A) $x = 5 , x = 18$
B) $x = 0.25 , x = 2.5$
C) $x = - 2.5 , x = 0.25$
D) $x = - 0.25 , x = 2.5$

Question 46

Use the graph of the function to estimate the x-intercepts.
$y=x^{2}-x-6$

A) $x = - 1 , x = - 6$
B) $x = - 3 , x = - 2$
C) $x = - 3 , x = 2$
D) $x = - 2 , x = 3$

Question 47

Use the graph of the function to estimate the x-intercepts.
$y=-x^{2}+2 x+35$

A) $x = - 5 , x = 7$
B) $x = 5 , x = 7$
C) $x = - 7 , x = 5$
D) $x = - 35 , x = - 2$

Question 48

The manager of big box store has found that if the price of a pillow is $\mathrm { p } ( \mathrm { x } ) = 95 - \frac { \mathrm { x } } { 8 }$ , then $\mathrm { x }$ pillows will be sold.
The expression for the total revenue from the sale of $x$ pillows is $R ( x ) = 95 x - \frac { x ^ { 2 } } { 8 }$ . Find the number of pillows that will produce maximum revenue.

A) 360 pillows
B) 420 pillows
C) 760 pillows
D) 380 pillows

Question 49

If a ball is thrown upward at 64 feet per second from the top of a building that is 110 feet high, the height of the ball can be modeled by $S = 110 + 64 t - 16 t ^ { 2 }$ feet, where t is the number of seconds after the ball is thrown. What
Is the ball's maximum height?

A) 302 ft
B) 110 ft
C) 158 ft
D) 174 ft

Question 50

Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c ( x ) = 4 x ^ { 2 } - 288 x + 50$ where x is the number of watches repaired. How many watches must he repair to have the lowest cost?

A) 50 watches
B) 36 watches
C) 25 watches
D) 40 watches

Question 51

Given the following revenue and cost functions, find the maximum profit. (Recall that profit equals revenue minus cost.) $R ( x ) = 80 x - 2 x ^ { 2 } ; C ( x ) = 24 x + 100$

A) $492
B) $684
C) $292
D) $392

Question 52

Use the graph of the function to estimate the x-intercepts.
$f(x)=4 x^{2}-19 x-5$

A) $x = - 0.25 , x = 5$
B) $x = - 1 , x = 20$
C) $x = - 5 , x = 0.25$
D) $x = 4 , x = - 5$

Question 53

Given the following revenue and cost functions, find the x-value that makes revenue a maximum. $R ( x ) = 84 x - 2 x ^ { 2 } ; C ( x ) = 22 x + 101$

A) 22
B) 21
C) 20
D) 42

Question 54

John owns a hot dog stand. His profit, in dollars, is given by the equation $P ( x ) = P = - x ^ { 2 } + 14 x + 59$ , where x is the number of hot dogs sold. What is the most he can earn?

A) $150
B) $108
C) $49
D) $87

Question 55

John owns a hot dog stand. He has found that his profit is given by the equation $P = - x ^ { 2 } + 80 x + 87$ , where x is the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

A) 23 hot dogs
B) 47 hot dogs
C) 40 hot dogs
D) 41 hot dogs

Question 56

If a ball is thrown upward at 64 feet per second from the top of a building that is 120 feet high, the height of the ball can be modeled by $\mathrm { S } = 120 + 64 \mathrm { t } - 16 \mathrm { t } ^ { 2 }$ feet, where t is the number of seconds after the ball is thrown. After
How many seconds does the ball reach its maximum height?

A) 2 sec
B) 4 sec
C) 1 sec
D) 3.8 sec

Question 57

Use the graph of the function to estimate the x-intercepts.
$y=x^{2}+3 x-18$

A) $x = - 6 , x = 3$
B) $x = - 3 , x = 6$
C) $x = - 3 , x = 18$
D) $x = 0$

Question 58

The profit for a product is given by $\mathrm { p } = 2204 + \mathrm { x } ^ { 2 } - 105 \mathrm { x }$ x, where x is the number of units produced and sold. Graphically find the x-intercepts of this function to find how many units will give break-even (that is return a
Profit of zero).

A) 29 units
B) 76 units
C) 29 or 76 units
D) They will never break even.

Question 59

Use the graph of the function to estimate the x-intercepts.
$g(x)=2 x^{2}+5 x-3$

A) $x = - 0.5 , x = 3$
B) $x = - 3 , x = 0.5$
C) $x = - 2 , x = 3$
D) $x = - 3 , x = - 0.5$

Question 60

Use the graph of the function to estimate the x-intercepts.
At Allied Electronics, production has begun on the $X - 15$ Computer Chip. The total revenue function is given by $R ( x ) = 50 x - 0.3 x ^ { 2 }$ and the total cost function is given by $C ( x ) = 8 x + 10$ , where $x$ represents the number of boxes of computer chips produced. The total profit function, $P ( x )$ , is such that $P ( x ) = R ( x ) - C ( x )$ . Find $P ( x )$ .

A) $P ( x ) = - 0.3 x ^ { 2 } + 42 x - 10$
B) $\mathrm { P } ( \mathrm { x } ) = 0.3 \mathrm { x } ^ { 2 } + 42 \mathrm { x } - 20$
C) $P ( x ) = - 0.3 x ^ { 2 } + 34 x + 10$
D) $\mathrm { P } ( \mathrm { x } ) = 0.3 \mathrm { x } ^ { 2 } + 34 \mathrm { x } - 30$

Question 61

Use factoring to
$12 \mathrm {~d} ^ { 2 } + 38 \mathrm {~d} + 30 = 0$

A) $\frac { 2 } { 3 } , \frac { 3 } { 5 }$
B) $- \frac { 2 } { 3 } , - \frac { 5 } { 3 }$
C) $- \frac { 3 } { 2 } , - \frac { 5 } { 3 }$
D) $\frac { 3 } { 2 } , \frac { 5 } { 3 }$

Question 62

Use factoring to
$$9 m ^ { 2 } - 8 m = 0$$

A) 0
B) $\frac { 8 } { 9 } , - \frac { 8 } { 9 }$
C) $\frac { 8 } { 9 } , 0$
D) $- \frac { 8 } { 9 } , 0$

Question 63

Use a graphing utility as an aid in factoring to
$$22 x ^ { 2 } + 129 x + 44 = 0$$

A) $x = \frac { 11 } { 2 } , x = - 4$
B) $x = - 11 , x = - \frac { 4 } { 11 }$
C) $x = - \frac { 11 } { 2 } , x = - \frac { 4 } { 11 }$
D) $x = \frac { 11 } { 2 } , x = \frac { 4 } { 11 }$

Question 64

Your company uses the quadratic model y $y = - 4.5 x ^ { 2 } + 150 x$ 150x to represent the average number of new customers who will be signed on (x) weeks after the release of your new service. How many new customers can you
Expect to gain in week 2?

A) 291 customers
B) 141 customers
C) 132 customers
D) 282 customers

Question 65

Use factoring to
$$3 k ^ { 2 } - 11 k - 4 = 0$$

A) $- \frac { 1 } { 3 } , 3$
B) $- 3,4$
C) $\frac { 1 } { 11 } , - \frac { 1 } { 3 }$
D) $- \frac { 1 } { 3 } , 4$

Question 66

The polynomial function $\mathrm { I } ( \mathrm { t } ) = - 0.1 \mathrm { t } ^ { 2 } + 1.4 \mathrm { t }$ represents the yearly income (or loss) from a real estate investment, where t is time in years. After how many years does income begin to decline?

A) 6 yr
B) 14 yr
C) 7 yr
D) 9.33 yr

Question 67

Use factoring to
$$3 x ^ { 2 } - 23 x = 8$$

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

Question 68

If a ball is thrown upward at 19.6 meters per second from the top of a building that is 70 meters high, the height of the ball can be modeled by $S = 70 + 19.6 t - 4.9 t ^ { 2 }$ meters, where t is the number of seconds after the ball is
Thrown. What is the ball's maximum height?

A) 70 m
B) 128.8 m
C) 84.7 m
D) 89.6 m

Question 69

Use factoring to
$$6 n ^ { 2 } + 14 n = 0$$
$\mathrm { A } ) = \frac { 7 } { 3 } , 14$
B) $- \frac { 7 } { 3 }$
C) 0
D) $- \frac { 7 } { 3 } , 0$

Question 70

Use a graphing utility to find or approximate the x-intercepts of the graph of the quadratic function.
$$y = x ^ { 2 } + 6 x + 8$$

A) $( - 2,0 ) , ( - 4,0 )$
B) $( 2,0 ) , ( 4,0 )$
C) $( 12,0 ) , ( - 4,0 )$
D) $( \sqrt { 8 } , 0 ) ( - \sqrt { 8 } , 0 )$

Question 71

Use factoring to
$$x ^ { 2 } + 10 x = - 16$$

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

Question 72

The average number of prisoners in a county jail is modeled by y $y = 0.15 x ^ { 2 } + 10.34 x + 114.16$ , where x is the number of years after 2000.

A) Graph this function from 0 to 30.
B) Approximate, to the nearest whole number, how many prisoners there will be in 2010.
C) Does this model indicate that the number of prisoners will increase or decrease from 2000 to 2030? A) a.

b. 233
c. increase
B) a.


b. 351
c. increase
C) a.

b. 233
c. increase
D) a.


b. 333
c. increase

Question 73

Use factoring to
$$4 x ^ { 2 } - 24 x + 32 = 0$$

A) $4,2,4$
B) 2,4
C) $- 2 , - 4$
D) $0,2,4$

Question 74

Use factoring to
$25 k ^ { 2 } - 4 = 0$

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

Question 75

Use factoring to
$$20 y ^ { 2 } + 41 y + 20 = 0$$

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

Question 76

Use a graphing utility to find or approximate the x-intercepts of the graph of the quadratic function.
$$y = 3 x ^ { 2 } + 8 x - 16$$

A) $( - 4,0 )$
B) $( - 4,0 )$ and $\left( \frac { 4 } { 3 } , 0 \right)$
C) No x-intercepts
D) $( 4,0 )$ and $\left( - \frac { 4 } { 3 } , 0 \right)$

Question 77

Use factoring to
$$x ^ { 2 } + 2 x - 3 = 0$$

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

Question 78

Use a graphing utility as an aid in factoring to
$$2 s ^ { 2 } - 136 s = - 1800$$

A) $\mathrm { s } = 50 , \mathrm {~s} = - 18$
B) $\mathrm { s } = 5 , \mathrm {~s} = 180$
C) $\mathrm { s } = 50 , \mathrm {~s} = 18$
D) $\mathrm { s } = 37 , \mathrm {~s} = 20$

Question 79

Use a graphing utility to find or approximate the x-intercepts of the graph of the quadratic function.
$$y = 9 k ^ { 2 } - 62 k - 7$$

A) $\left( \frac { 1 } { 62 } , 0 \right) , \left( - \frac { 1 } { 9 } , 0 \right)$
B) $\left( - \frac { 1 } { 9 } , 0 \right)$ ,
C) $\left( - \frac { 1 } { 9 } , 0 \right) , ( 7,0 )$
D) $( - 9,0 ) , ( 7,0 )$

Question 80

If 5000 feet of fencing are used to enclose a rectangular field, the resulting area of the field is A=x(2500-x) , where x is the width of the pen. What is the maximum possible area of the pen?

A) 62,500ft²
B) 1,562,500ft²
C) 1250ft²
D) 31,250ft²