Deck 4: Polynomial and Rational Functions

Question 1

Find the y-intercept for the graph of the quadratic function.
$$f ( x ) = ( x + 2 ) ^ { 2 } - 4$$

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

Answer 1

D

Question 2

Find the x-intercepts (if any)for the graph of the quadratic function.
$$f ( x ) = ( x - 3 ) ^ { 2 } - 9$$

A) $( 0,0 )$ and $( 6,0 )$
B) $( 0,0 )$ and $( - 9,0 )$
C) $( 0,0 )$ and $( - 6,0 )$
D) $( - 6,0 )$ and $( 6,0 )$

Answer 2

A

Question 3

Sketch the graph of the quadratic function.
$$f ( x ) = x ^ { 2 } - 6 x - 9$$

A) $( 3 , - 18 )$
В) $( - 3,18 )$
C) $( 3 , - 36 )$
D) $( - 6,63 )$

Answer 3

A

Question 4

Find the coordinates of the vertex of the quadratic function.
$$f ( x ) = - x ^ { 2 } - 4 x + 6$$

A) $x = 2$
B) $x = - 2$
C) $x = - 4$
D) $x = 10$

Question 5

Find the y-intercept for the graph of the quadratic function.
A)

B)

C)

D)

Question 6

Find the y-intercept for the graph of the quadratic function.
$$f ( x ) = ( x + 4 ) ^ { 2 } + 6$$

A)


B)


C)

D)

Question 7

Find the range of the quadratic function in interval notation.
$$f ( x ) = - 7 ( x - 3 ) ^ { 2 } - 6$$

A) $( - \infty , - 6 ]$
В) $[ - 6 , \infty )$
C) $( - \infty , 3 ]$
D) $[ - 3 , \infty )$

Question 8

The logistic growth functi models the number of people who have become ill with a
$$f ( x ) = ( x + 2 ) ^ { 2 } + 8$$

A) $[ 2 , \infty )$
B) $[ - 2 , \infty )$
C) $[ - 8 , \infty )$
D) $[ 8 , \infty )$

Question 9

Find the range of the quadratic function in interval notation.
$$f ( x ) = x ^ { 2 } - 4$$

A) $( - 4,0 )$
B) $( 2,0 )$
C) $( - 2,0 )$ and $( 2,0 )$
D) No x-intercepts

Question 10

The logistic growth functi describes the population of a species of butterflies t months
$$f ( x ) = 11 ( x - 4 ) ^ { 2 } + 6$$

A) $x = - 4$
B) $x = 4$
C) $x = 6$
D) $x = 11$

Question 11

Sketch the graph of the quadratic function.
$$f ( x ) = - x ^ { 2 } - 8 x + 1$$

A) $( - 8,1 )$
B) $( - 4,17 )$
C) $( 4 , - 47 )$
D) $( 4 , - 15 )$

Question 12

Find the coordinates of the vertex of the quadratic function.
$$f ( x ) = - 4 x ^ { 2 } - 8 x - 9$$

A) $( 1 , - 21 )$
B) $( 2 , - 41 )$
C) $( - 2 , - 17 )$
D) $( - 1 , - 5 )$

Question 13

The logistic growth functi models the number of people who have become ill with a
$$f ( x ) = 11 ( x - 3 ) ^ { 2 } + 8$$

A) $[ - 8 , \infty )$
B) $( - \infty , 8 ]$
C) $[ 8 , \infty )$
D) $[ 3 , \infty )$

Question 14

The logistic growth functi models the number of people who have become ill with a
$$f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 5$$

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

Question 15

The logistic growth functi describes the population of a species of butterflies t months
$$f ( x ) = - ( x + 3 ) ^ { 2 } + 9$$

A) $x = - 9$
B) $x = 3$
C) $x = - 3$
D) $x = 9$

Question 16

The logistic growth functi describes the population of a species of butterflies t months
$$f ( x ) = ( x + 4 ) ^ { 2 } - 6$$

A) $x = - 4$
B) $x = 6$
C) $x = 4$
D) $x = - 6$

Question 17

Find the coordinates of the vertex of the quadratic function.
$$f ( x ) = x ^ { 2 } - 4 x - 1$$

A) $x = 2$
B) $x = - 4$
C) $x = - 5$
D) $x = - 2$

Question 18

Sketch the graph of the quadratic function.
$$f ( x ) = 1 - ( x + 1 ) ^ { 2 }$$

A)

B)

C)

D)

Question 19

The logistic growth functi models the number of people who have become ill with a
$$f ( x ) = ( x + 4 ) ^ { 2 } - 9$$

A) $[ - 4 , \infty )$
B) $( - \infty , - 4 ]$
C) $( - \infty , - 9 ]$
D) $[ - 9 , \infty )$

Question 20

The logistic growth functi models the number of people who have become ill with a
$$f ( x ) = - ( x + 4 ) ^ { 2 } + 5$$

A) $( - \infty , 4 ]$
B) $( - \infty , 5 ]$
C) $[ - 4 , \infty )$
D) $[ 5 , \infty )$

Question 21

Rewrite the quadratic function in standard form by completing the square.
$$f ( x ) = - 9 x ^ { 2 } - 2 x - 12$$

A) No x-intercepts; No $y$ -intercepts
B) x-intercepts: $- \frac { 1 } { 9 }$ and $- \frac { 107 } { 9 } ; y$ -intercept: 12
C) $x$ -intercepts: $\frac { 1 } { 9 }$ and $\frac { 107 } { 9 } ; y$ -intercept: $- 12$
D) No $x$ -intercepts; $y$ -intercept: $- 12$

Question 22

Find the axis of symmetry of the quadratic function.
$$f ( x ) = x ^ { 2 } - 8 x$$

A) $f ( x ) = ( x + 8 ) ^ { 2 } - 8$
B) $f ( x ) = ( x + 4 ) ^ { 2 } - 4$
C) $f ( x ) = ( x - 4 ) ^ { 2 } - 16$
D) $f ( x ) = ( x - 8 ) ^ { 2 } - 64$

Question 23

Find the axis of symmetry of the quadratic function.
$$f ( x ) = x ^ { 2 } + 6 x - 4$$

A) $f ( x ) = ( x + 6 ) ^ { 2 } - 40$
B) $f ( x ) = ( x + 3 ) ^ { 2 } + 13$
C) $f ( x ) = ( x + 3 ) ^ { 2 } - 13$
D) $f ( x ) = ( x + 6 ) ^ { 2 } + 40$

Question 24

Find the axis of symmetry of the quadratic function.
$$f ( x ) = x ^ { 2 } - 6 x + 7$$

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

Question 25

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts.
$$f ( x ) = x ^ { 2 } + 8 x + 6$$

A) $( - \infty , - 42 ]$
B) $[ - 10 , \infty )$
C) $[ 4 , \infty )$
D) $( - \infty , - 10 ]$

Question 26

Rewrite the quadratic function in standard form by completing the square.
$f ( x ) = x ^ { 2 } + 18 x + 66 \quad$ Give your answers in exact form.

A) x-intercepts: $- 9 - \sqrt { 15 }$ and $- 9 + \sqrt { 15 } ; y$ -intercept: 66
B) x-intercepts: $- 18 - \sqrt { 66 }$ and $- 18 + \sqrt { 66 } ;$ y-intercept: $- 66$
C) x-intercepts: $9 - \sqrt { 66 }$ and $9 + \sqrt { 66 } ; y$ -intercept: 66
D) $x$ -intercepts: $9 + \sqrt { 15 } ; y$ -intercept: $- 66$

Question 27

Rewrite the quadratic function in standard form by completing the square.
$$f ( x ) = 2 x ^ { 2 } + 10 x - 48$$

A) $x$ -intercepts: 6 and 4 ; No $y$ -intercepts
B) x-intercepts: 6 and $- 4 ; y$ -intercept: $- 10$
C) $x$ -intercepts: $- 8$ and 3 ; $y$ -intercept: $- 48$
D) $x$ -intercepts: $- 8$ and $- 3 ; y$ -intercept: 48

Question 28

Rewrite the quadratic function in standard form by completing the square.
$$f ( x ) = - x ^ { 2 } + 17 x - 72$$

A) $x$ -intercepts: 8 and $- 9 ; y$ -intercept: 17
B) $x$ -intercepts: $- 8$ and $- 9 ; y$ -intercept: 72
C) $x$ -intercepts: 8 and $9 ; y$ -intercept: $- 72$
D) No x-intercepts; y-intercept: $- 72$

Question 29

Find the axis of symmetry of the quadratic function.
$$f ( x ) = x ^ { 2 } + 3 x + 1$$

A) $f ( x ) = \left( x + \frac { 3 } { 2 } \right) ^ { 2 } + \frac { 5 } { 4 }$
B) $f ( x ) = ( x + 3 ) ^ { 3 } - 9$
C) $f ( x ) = ( x - 3 ) ^ { 3 } - 9$
D) $f ( x ) = \left( x + \frac { 3 } { 2 } \right) ^ { 2 } - \frac { 5 } { 4 }$

Question 30

Rewrite the quadratic function in standard form by completing the square.
$$f ( x ) = 2 x ^ { 2 } + 28 x + 90$$

A) $x$ -intercepts: $- 5$ and 9 ; $y$ -intercept: 0
B) x-intercepts: 5 and $9 ; y$ -intercept: $- 90$
C) $x$ -intercepts: $- 5$ and $- 9 ; y$ -intercept: 90
D) $x$ -intercepts: 5 and $- 9 ; y$ -intercept: $- 28$

Question 31

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts.
$f ( x ) = 3 x ^ { 2 } + 10 x + 4 \quad$ Give your answers in exact form.

A) $x$ -intercepts: $\frac { - 10 - \sqrt { 13 } } { 3 }$ and $\frac { - 10 + \sqrt { 13 } } { 3 } ; y$ -intercept: 0
B) x-intercepts: $\frac { - 5 - \sqrt { 13 } } { 6 }$ and $\frac { - 5 + \sqrt { 13 } } { 6 } ; y$ -intercept: 4
C) $x$ -intercepts: $\frac { - 5 - \sqrt { 13 } } { 3 }$ and $\frac { - 5 - \sqrt { 13 } } { 3 } ; y$ -intercept: 4
D) $x$ -intercepts: $\frac { - 5 - \sqrt { 37 } } { 3 }$ and $\frac { - 5 + \sqrt { 37 } } { 3 } ; y$ -intercept: 0

Question 32

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts.
$$f ( x ) = - x ^ { 2 } + 14 x + 2$$

A) $[ 7 , \infty )$
B) $( - \infty , 7 ]$
C) $( - \infty , 51 ]$
D) $[ 51 , \infty )$

Question 33

Find the axis of symmetry of the quadratic function.
$$f ( x ) = - 3 x ^ { 2 } - 6 x + 8$$

A) $x = - 2$
B) $x = - 1$
C) $x = 1$
D) $x = 11$

Question 34

Find the axis of symmetry of the quadratic function.
$$f ( x ) = x ^ { 2 } - 18 x$$

A) $f ( x ) = ( x + 18 ) ^ { 2 } - 18$
B) $f ( x ) = ( x - 18 ) ^ { 2 } - 324$
C) $f ( x ) = ( x + 9 ) ^ { 2 } - 9$
D) $f ( x ) = ( x - 9 ) ^ { 2 } - 81$

Question 35

Rewrite the quadratic function in standard form by completing the square.
$$f ( x ) = x ^ { 2 } + 5 x + 2$$

A) $f ( x ) = \left( x + \frac { 5 } { 2 } \right) ^ { 2 } - \frac { 17 } { 4 }$
B) $f ( x ) = \left( x - \frac { 5 } { 2 } \right) ^ { 2 } + \frac { 17 } { 4 }$
C) $f ( x ) = ( x - 5 ) ^ { 2 } + 23$
D) $f ( x ) = ( x + 5 ) ^ { 2 } - 23$

Question 36

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts.
$$f ( x ) = 4 x ^ { 2 } - 2 x - 9$$

A) $\left[ \frac { 1 } { 4 } , \infty \right)$
B) $\left( - \infty , - \frac { 37 } { 4 } \right]$
C) $\left[ - \frac { 37 } { 4 } , \infty \right)$
D) $\left( - \infty , \frac { 1 } { 4 } \right]$

Question 37

Rewrite the quadratic function in standard form by completing the square.
$$f ( x ) = x ^ { 2 } + 3 x + 2$$

A) $x$ -intercepts: $- 1$ and $2 ; y$ -intercept: 2
B) x-intercepts: $- 1$ and -2; y-intercept: 2
C) x-intercepts: 1 and 2; $y$ -intercept: $- 1$
D) $x$ -intercepts: 1 and -2; $y$ -intercept: 0

Question 38

Find the axis of symmetry of the quadratic function.
$$f ( x ) = 3 x ^ { 2 } - 4 x$$

A) $f ( x ) = 3 \left( x - \frac { 2 } { 3 } \right) ^ { 2 } - \frac { 4 } { 3 }$
B) $f ( x ) = 3 \left( x - \frac { 2 } { 3 } \right) ^ { 2 } + \frac { 4 } { 9 }$
C) $f ( x ) = 3 \left( x + \frac { 4 } { 3 } \right) ^ { 2 } + \frac { 16 } { 9 }$
D) $f ( x ) = 3 \left( x + \frac { 4 } { 3 } \right) ^ { 2 } - \frac { 16 } { 9 }$

Question 39

Rewrite the quadratic function in standard form by completing the square.
$$f ( x ) = x ^ { 2 } + 12 x + 36$$

A)x-intercepts: 6; y-intercept: 36
B)No x-intercepts; y-intercept: 72
C)x-intercepts: -6; y-intercept: 36
D)x-intercepts: -6; y-intercept: 72

Question 40

Find the axis of symmetry of the quadratic function.
$$f ( x ) = x ^ { 2 } + 10 x + 33$$

A) $f ( x ) = ( x - 5 ) ^ { 2 } - 8$
B) $f ( x ) = ( x - 5 ) ^ { 2 } + 8$
C) $f ( x ) = ( x + 5 ) ^ { 2 } - 8$
D) $f ( x ) = ( x + 5 ) ^ { 2 } + 8$

Question 41

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts.
$$f ( x ) = - 2 x ^ { 2 } - 4 x$$

A) $( - \infty , 2 ]$
B) $( - \infty , - 2 ]$
C) $( - \infty , 1 ]$
D) $( - \infty , - 1 ]$

Question 42

Graph the quadratic function using its vertex, axis of symmetry, and intercepts.
A) vertex $( 3 , - 1 )$
intercepts $( 4,0 ) , ( 2,0 ) , ( 0,8 )$

B) vertex $( - 3 , - 1 )$
intercepts $( - 4,0 ) , ( - 2,0 ) , ( 0,8 )$

C) vertex $( 3,1 )$
intercepts $( 4,0 ) , ( 2,0 ) , ( 0 , - 8 )$

D) vertex $( - 3,1 )$
intercepts $( - 4,0 ) , ( - 2,0 ) , ( 0 , - 8 )$

Question 43

Graph the quadratic function using its vertex, axis of symmetry, and intercepts.
$$f ( x ) = x ^ { 2 } + 2 x - 8$$

A) vertex $( 1,9 )$
intercepts $( - 2,0 ) , ( 4,0 ) , ( 0,8 )$

B) vertex $( 1 , - 9 )$
intercepts $( - 2,0 ) , ( 4,0 ) , ( 0 , - 8 )$

C) vertex $( - 1 , - 9 )$
intercepts $( 2,0 ) , ( - 4,0 ) , ( 0 , - 8 )$

D) vertex $( - 1,9 )$
intercepts $( 2,0 ) , ( - 4,0 ) , ( 0,8 )$

Question 44

Find the range of the quadratic function in interval notation.
$$f ( x ) = - 3 x ^ { 2 } + 36 x - 102$$

A) minimum at $( - 6,0 )$
B) minimum at $( 0 , - 6 )$
C) maximum: $( 6,6 )$
D) maximum at $( - 6 , - 6 )$

Question 45

Graph the quadratic function using its vertex, axis of symmetry, and intercepts.
$(x)=-x^{2}+2 x$

A) vertex $( - 1 , - 1 )$
intercept $( 0 , - 2 )$

B) vertex $( - 1,1 )$
intercepts $( 0,0 ) , ( - 2,0 )$

C) vertex $( 1 , - 1 )$
intercept $( 0 , - 2 )$

D) vertex $( 1,1 )$
intercepts $( 0,0 ) , ( 2,0 )$

Question 46

Find the range of the quadratic function in interval notation.
$$f ( x ) = x ^ { 2 } + 4 x - 3$$

A) maximum at $( - 7 , - 2 )$
B) minimum at $( - 2 , - 7 )$
C) maximum at $( 0 , - 2 )$
D) minimum at $( - 7,0 )$

Question 47

Find the range of the quadratic function in interval notation.
$$f ( x ) = 4 x ^ { 2 } + 8 x$$

A) minimum at $( - 1 , - 4 )$
B) maximum at $( 1 , - 4 )$
C) minimum; (ii) $( 1 , - 4 )$
D) maximum at $( - 1 , - 4 )$

Question 48

Find the range of the quadratic function in interval notation.
$$f ( x ) = x ^ { 2 } - 18 x + 87$$

A) minimum at $( 9,6 )$
B) maximum at $( 6,0 )$
C) maximum at $( 6,9 )$
D) minimum at $( 0,9 )$

Question 49

Graph the quadratic function using its vertex, axis of symmetry, and intercepts.
$$f ( x ) = x ^ { 2 } + 12 x + 36$$

A) vertex $( - 6,0 )$
intercepts $( 0,36 ) , ( - 6,0 )$

B) vertex $( - 6,36 )$
intercept $( 0,72 )$

C) vertex $( 6,0 )$
intercepts $( 0,36 ) , ( 6,0 )$

D) vertex $( 6,36 )$
intercept $( 0,72 )$

Question 50

Find the range of the quadratic function in interval notation.
$$f ( x ) = 3 x ^ { 2 } + 3 x - 9$$

A) minimum at $\left( - \frac { 1 } { 2 } , - \frac { 39 } { 4 } \right)$
B) minimum at $\left( - \frac { 39 } { 4 } , - \frac { 1 } { 2 } \right)$
C) maximum at $\left( - \frac { 1 } { 2 } , - \frac { 39 } { 4 } \right)$
D) maximum at $\left( - \frac { 39 } { 4 } , - \frac { 1 } { 2 } \right)$

Question 51

Find the range of the quadratic function in interval notation.
$$f ( x ) = 9 x ^ { 2 } + 36 x + 27$$

A) maximum at $( - 9 , - 2 )$
B) minimum at $( - 2,0 )$
C) maximum at $( - 9,0 )$
D) minimum at $( - 2 , - 9 )$

Question 52

Find the range of the quadratic function in interval notation.
$$f ( x ) = - x ^ { 2 } - 4 x - 7$$

A) maximum at (-2,-3)
B) minimum at $( 3,0 )$
C) minimum at $( 0,2 )$
D) maximum at $( 3,2 )$

Question 53

Graph the quadratic function using its vertex, axis of symmetry, and intercepts.
A) vertex $( - 3 , - 1 )$
intercepts $( - 4,0 ) , ( - 2,0 ) , ( 0,8 )$

B) vertex $( 3,1 )$
intercepts $( 4,0 ) , ( 2,0 ) , ( 0 , - 8 )$

D) vertex $( 3 , - 1 )$
intercepts $( 4,0 ) , ( 2,0 ) , ( 0,8 )$

C) vertex $( - 3,1 )$
intercepts $( - 4,0 ) , ( - 2,0 ) , ( 0 , - 8 )$

Question 54

Find the range of the quadratic function in interval notation.
$$f ( x ) = 3 x ^ { 2 } - 36 x + 113$$

A) maximum at $( 5,6 )$
B) minimum at $( 6,5 )$
C) minimum at $( 6,0 )$
D) maximum at $( 5,0 )$

Question 55

Graph the quadratic function using its vertex, axis of symmetry, and intercepts.
$f(x)=-x^{2}-4 x-3$

A) vertex $( - 2,1 )$
intercepts $( - 1,0 ) , ( - 3,0 ) , ( 0 , - 3 )$

B) vertex $( - 2 , - 1 )$
intercepts $( - 1,0 ) , ( - 3,0 ) , ( 0,3$

C) vertex $( 2,1 )$
intercepts $( 1,0 ) , ( 3,0 ) , ( 0 , - 3 )$

D) vertex $( 2 , - 1 )$
intercepts $( 1,0 ) , ( 3,0 ) , ( 0,3 )$

Question 56

Find the range of the quadratic function in interval notation.
$$f ( x ) = - 2 x ^ { 2 } - 12 x - 27$$

A) minimum at $( 9,0 )$
B) minimum at $( 0,3 )$
C) maximum at $( 9,3 )$
D) maximum at $( - 3 , - 9 )$

Question 57

Graph the quadratic function using its vertex, axis of symmetry, and intercepts.
$f(x)=x^{2}-6 x$

A) vertex $( 3,9 )$
intercept $( 0,18 )$

B) vertex $( - 3,9 )$
intercept $( 0,18 )$

C) vertex $( - 3 , - 9 )$
intercepts $( 0,0 ) , ( - 6,0 )$

D) vertex $( 3 , - 9 )$
intercepts $( 0,0 ) , ( 6,0 )$

Question 58

Find the range of the quadratic function in interval notation.
A) vertex $\left( - \frac { 1 } { 10 } , \frac { 69 } { 10 } \right)$
intercept $( 0,7 )$

B) vertex $\left( - \frac { 1 } { 10 } , - \frac { 69 } { 10 } \right)$
intercept $( 0 , - 7 )$

C) vertex $\left( \frac { 1 } { 10 } , - \frac { 69 } { 10 } \right)$
intercept $( 0 , - 7 )$

D) vertex $\left( \frac { 1 } { 10 } , \frac { 69 } { 10 } \right)$

intercept $( 0,7 )$

Question 59

Graph the quadratic function using its vertex, axis of symmetry, and intercepts.
$$f ( x ) = 4 x ^ { 2 } - 8 x + 8$$

A) vertex $( - 1,4 )$
intercept $( 0,8 )$

B) vertex $( 1,4 )$
intercept $( 0,8 )$

C) vertex $( - 1,4 )$
intercept $\left( 0 , \frac { 17 } { 4 } \right)$

D) vertex $( 1,4 )$
intercept $\left( 0 , \frac { 17 } { 4 } \right)$

Question 60

Find the range of the quadratic function in interval notation.
$$f ( x ) = x ^ { 2 } + 6 x + 3$$

A) minimum at $( - 3 , - 6 )$
B) minimum at $( 0 , - 3 )$
C) maximum at $( - 6 , - 3 )$
D) maximum at $( - 6,0 )$

Question 61

Write the equation of the function in the form f(x)= ax2 + bx + c.

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

Question 62

Solve the problem.
Consider the quadratic model $h ( t ) = - 16 t ^ { 2 } + 40 t + 50$ for the height (in feet), $h$ , of an object $t$ seconds after the object has been projected straight up into the air. Find the maximum height attained by the object. How much time does it take to fall back to the ground? Assume that it takes the same time for going up and coming down.

A)maximum height = 75 ft; time to reach ground = 2.5 seconds
B)maximum height = 50 ft; time to reach ground = 1.25 seconds
C)maximum height = 75 ft; time to reach ground = 1.25 seconds
D)maximum height = 50 ft; time to reach ground = 2.5 seconds

Question 63

Solve the problem.
The owner of a video store has determined that the profits P of the store are approximately given by $$P ( x ) = - x ^ { 2 } + 50 x + 62$$ where x is the number of videos rented daily. Find the maximum profit to the nearest dollar.

A)$1312
B)$625
C)$1250
D)$687

Question 64

Find the range of the quadratic function in interval notation.
$$f ( x ) = \frac { 1 } { 2 } x ^ { 2 } + 4 x - 4$$

A) minimum at $( - 4 , - 12 )$
B) maximum at $( 4,6 )$
C) minimum at $( 4,12 )$
D) maximum at $( - 4 , - 4 )$

Question 65

Solve the problem.
The owner of a video store has determined that the cost C, in dollars, of operating the store is approximately given by $$C ( x ) = 2 x ^ { 2 } - 28 x + 600$$ , where x is the number of videos rented daily. Find the lowest cost to the nearest dollar.

A)$698
B)$502
C)$208
D)$404

Question 66

Write the equation of the function in the form f(x)= ax2 + bx + c.

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

Question 67

Solve the problem.
A projectile is fired from a cliff 600 feet above the water at an inclination of $45 ^ { \circ }$ to the horizontal, with a muzzle velocity of 120 feet per second. The height $h$ of the projectile above the water is given by $h ( x ) = \frac { - 32 x ^ { 2 } } { ( 120 ) ^ { 2 } } + x + 600$ , where $x$ is the horizontal distance of the projectile from the base of the cliff. How far from the base of the cliff is the height of the projectile a maximum?

A)712.5 ft
B)225 ft
C)937.5 ft
D)112.5 ft

Question 68

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value.
$$f ( x ) = - x ^ { 2 } - \frac { 4 } { 5 } x + 6$$

A) minimum at $\left( - \frac { 2 } { 5 } , - \frac { 121 } { 25 } \right)$
B) minimum at $\left( - \frac { 1 } { 10 } , - \frac { 73 } { 3 } \right)$
C) maximum at $\left( \frac { 1 } { 10 } , - 121 \right)$
D) maximum at $\left( - \frac { 2 } { 5 } , \frac { 154 } { 25 } \right)$

Question 69

Solve the problem.
The manufacturer of a CD player has found that the revenue R (in dollars)is $$R ( p ) = - 5 p ^ { 2 } + 1590 p$$ when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest whole dollar?

A)$252,810
B)$1,011,240
C)$505,620
D)$126,405

Question 70

Write the equation of the function in the form f(x)= ax2 + bx + c.

A) $y = - 2 ( x + 2 ) ^ { 2 } - 6$
B) $y = \frac { 1 } { 2 } ( x + 2 ) ^ { 2 } + 6$
C) $y = - \frac { 1 } { 2 } ( x + 2 ) ^ { 2 } - 6$
D) $y = 2 ( x + 2 ) ^ { 2 } + 6$

Question 71

Solve the problem.
The profit that the vendor makes per day by selling x pretzels is given by the function $$P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 150$$ Find the number of pretzels that must be sold to maximize profit.

A)400 pretzels
B)170 pretzels
C)800 pretzels
D)0.8 pretzels

Question 72

Write the equation of the function in the form f(x)= ax2 + bx + c.

A) $f ( x ) = - 2 ( x - 1 ) ^ { 2 } - 6$
B) $f ( x ) = 2 ( x - 1 ) ^ { 2 } - 6$
C) $f ( x ) = 2 ( x - 1 ) ^ { 2 } + 6$
D) $f ( x ) = 2 ( x + 1 ) ^ { 2 } + 6$

Question 73

Write the equation of the function in the form f(x)= ax2 + bx + c.

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

Question 74

Solve the problem.
A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 352 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed? A) $23,232 \mathrm { ft } ^ { 2 }$
B) $15,488 \mathrm { ft } ^ { 2 }$
C) $30,976 \mathrm { ft } ^ { 2 }$
D) $7744 \mathrm { ft } ^ { 2 }$

Question 75

Write the equation of the function in the form f(x)= ax2 + bx + c.

A) $f ( x ) = ( x + 2 ) ^ { 2 } - 4$
B) $f ( x ) = - ( x + 2 ) ^ { 2 } + 4$
C) $f ( x ) = ( x + 2 ) ^ { 2 } + 4$
D) $f ( x ) = - ( x + 2 ) ^ { 2 } - 4$

Question 76

Find the range of the quadratic function in interval notation.
$$f ( x ) = - 5 x ^ { 2 } - 10 x$$

A) minimum at $( 1 , - 5 )$
B) maximum at $( 1 , - 5 )$
C) maximum at $( - 1,5 )$
D) minimum at $( - 1,5 )$

Question 77

Solve the problem.
You have 192 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area.

A)96 ft by 24 ft
B)96 ft by 96 ft
C)50 ft by 46 ft
D)48 ft by 48 ft

Question 78

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value.

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

Question 79

Write the equation of the function in the form f(x)= ax2 + bx + c.

A) $f ( x ) = 2 ( x - 1 ) ^ { 2 } - 3$
B) $f ( x ) = - 2 ( x + 1 ) ^ { 2 } - 3$
C) $f ( x ) = 2 ( x + 1 ) ^ { 2 } + 3$
D) $f ( x ) = 2 ( x + 1 ) ^ { 2 } - 3$

Question 80

Solve the problem.
A projectile is fired from a cliff 200 feet above the water at an inclination of $45 ^ { \circ }$ to the horizontal, with a muzzle velocity of 380 feet per second. The height h of the projectile above the water is given by h $( x ) = \frac { - 32 x ^ { 2 } } { ( 380 ) ^ { 2 } } + x + 200$ , where $x$ is the horizontal distance of the projectile from the base of the cliff. Find the maximum height of the projectile.

A)2256.25 ft
B)3584.38 ft
C)1128.13 ft
D)1328.13 ft