Question 1

Determine whether the graph shown is the graph of a polynomial function.
-

Accepted Answer

A) polynomial function 
B) not a polynomial function 
A) polynomial function 
B) not a polynomial function

Question 2

Find the degree of the polynomial function.
-$$f ( x ) = 5 x - x ^ { 4 } + \frac { 5 } { 4 }$$

Accepted Answer

A)  1 
B)  5 
C)  $- 1$ 
D)  4 
A)  1 
B)  5 
C)  $- 1$ 
D)  4

Question 3

Solve the problem.
-Write an equation in standard form of the parabola that has the same shape as the graph of $f ( x ) = 5 x ^ { 2 }$, but which has a minimum of 6 at $x = 2$.

Accepted Answer

A)  $f ( x ) = 5 ( x + 6 ) ^ { 2 } - 2$ 
B)  $f ( x ) = 5 ( x + 2 ) ^ { 2 } + 6$ 
C)  $f ( x ) = - 5 ( x - 2 ) ^ { 2 } + 6$ 
D)  $f ( x ) = 5 ( x - 2 ) ^ { 2 } + 6$ 
A)  $f ( x ) = 5 ( x + 6 ) ^ { 2 } - 2$ 
B)  $f ( x ) = 5 ( x + 2 ) ^ { 2 } + 6$ 
C)  $f ( x ) = - 5 ( x - 2 ) ^ { 2 } + 6$ 
D)  $f ( x ) = 5 ( x - 2 ) ^ { 2 } + 6$

Question 4

Find the range of the quadratic function.
-$$f ( x ) = - x ^ { 2 } - 14 x + 8$$

Accepted Answer

A)  $[ - 7 , \infty )$ 
B)  $[ 57 , \infty )$ 
C)  $( - \infty , - 7 ]$ 
D)  $( - \infty , 57 ]$ 
A)  $[ - 7 , \infty )$ 
B)  $[ 57 , \infty )$ 
C)  $( - \infty , - 7 ]$ 
D)  $( - \infty , 57 ]$

Question 5

Solve the problem
-You have 120 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area.

Accepted Answer

A) 32 ft by 28 ft 
B) 60 ft by 60 ft 
C) 30 ft by 30 ft 
D) 60 ft by 15 ft 
A) 32 ft by 28 ft 
B) 60 ft by 60 ft 
C) 30 ft by 30 ft 
D) 60 ft by 15 ft

Question 6

Find the y-intercept for the graph of the quadratic function.
-$$f ( x ) = x ^ { 2 } + 5 x - 6$$

Accepted Answer

A)  $( 0,5 )$ 
B)  $( 0 , - 6 )$ 
C)  $( 0,3 )$ 
D)  $( 0,6 )$ 
A)  $( 0,5 )$ 
B)  $( 0 , - 6 )$ 
C)  $( 0,3 )$ 
D)  $( 0,6 )$

Question 7

Solve the problem
-A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 600 feet of fencing is used. Find the maximum area of the playground.

Accepted Answer

A)  $22,500 \mathrm { ft } ^ { 2 }$ 
B)  $16,875 \mathrm { ft } ^ { 2 }$ 
C)  $11,250 \mathrm { ft } ^ { 2 }$ 
D)  $15,000 \mathrm { ft } ^ { 2 }$ 
A)  $22,500 \mathrm { ft } ^ { 2 }$ 
B)  $16,875 \mathrm { ft } ^ { 2 }$ 
C)  $11,250 \mathrm { ft } ^ { 2 }$ 
D)  $15,000 \mathrm { ft } ^ { 2 }$

Question 8

Solve the problem
-The owner of a video store has determined that the profits $\mathrm { P }$ of the store are approximately given by $\mathrm { P } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 80 \mathrm { x } + 72$, where $\mathrm { x }$ is the number of videos rented daily. Find the maximum profit to the nearest dollar.

Accepted Answer

A)  $\$ 3200$ 
B)  $\$ 1600$ 
C)  $\$ 3272$ 
D)  $\$ 1672$ 
A)  $\$ 3200$ 
B)  $\$ 1600$ 
C)  $\$ 3272$ 
D)  $\$ 1672$

Question 9

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the
x-axis or touches the x-axis and turns around, at each zero.
-$$f ( x ) = 3 ( x + 2 ) ( x + 5 ) ^ { 2 }$$

Accepted Answer

A)  $- 2$, multiplicity 1 , crosses $x$-axis; $- 5$, multiplicity 2 , touches $x$-axis and turns around 
B)  2 , multiplicity 1 , touches $x$-axis and turns around; 5 , multiplicity 2 , crosses $x$-axis 
C)  2 , multiplicity 1 , crosses $x$-axis; 5 , multiplicity 2 , touches $x$-axis and turns around 
D)  $- 2$, multiplicity 1 , touches $x$-axis and turns around; $- 5$, multiplicity 2 , crosses $x$-axis 
A)  $- 2$, multiplicity 1 , crosses $x$-axis; $- 5$, multiplicity 2 , touches $x$-axis and turns around 
B)  2 , multiplicity 1 , touches $x$-axis and turns around; 5 , multiplicity 2 , crosses $x$-axis 
C)  2 , multiplicity 1 , crosses $x$-axis; 5 , multiplicity 2 , touches $x$-axis and turns around 
D)  $- 2$, multiplicity 1 , touches $x$-axis and turns around; $- 5$, multiplicity 2 , crosses $x$-axis

Question 10

Find the y-intercept of the polynomial function.
-$$f ( x ) = ( x + 1 ) ( x - 9 ) ( x - 1 ) ^ { 2 }$$

Accepted Answer

A)  9 
B)  -1 
C)  $- 9$ 
D)  0 
A)  9 
B)  -1 
C)  $- 9$ 
D)  0

Question 11

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior
to match the function with its graph.
-$$f ( x ) = - 3 x ^ { 2 } + 3 x - 3$$

Accepted Answer

A)  rises to the left and falls to the right
  
B)  rises to the left and rises to the right
  
C)  falls to the left and rises to the right
  
D)  falls to the left and falls to the right
  
A)  rises to the left and falls to the right
  
B)  rises to the left and rises to the right
  
C)  falls to the left and rises to the right
  
D)  falls to the left and falls to the right

Question 12

Use the vertex and intercepts to sketch the graph of the quadratic function.
-$f ( x ) = ( x + 5 ) ^ { 2 } + 6$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 13

Find the range of the quadratic function.
-$$f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 9$$

Accepted Answer

A)  $[ - 2 , \infty )$ 
B)  $[ - 9 , \infty )$ 
C)  $( - \infty , - 9 ]$ 
D)  $( - \infty , 2 ]$ 
A)  $[ - 2 , \infty )$ 
B)  $[ - 9 , \infty )$ 
C)  $( - \infty , - 9 ]$ 
D)  $( - \infty , 2 ]$

Question 14

Find the range of the quadratic function.
-$$y + 4 = ( x + 2 ) ^ { 2 }$$

Accepted Answer

A)  $[ 4 , \infty )$ 
B)  $[ - 4 , \infty )$ 
C)  $( - \infty , 4 ]$ 
D)  $( - \infty , 2 ]$ 
A)  $[ 4 , \infty )$ 
B)  $[ - 4 , \infty )$ 
C)  $( - \infty , 4 ]$ 
D)  $( - \infty , 2 ]$

Question 15

Solve the problem
-An object is propelled vertically upward from the top of a 32 -foot building. The quadratic function $s ( t ) = - 16 t ^ { 2 } + 160 t + 32$ models the ball's height above the ground, $s ( t )$, in feet, $t$ seconds after it was thrown. How many seconds does it take until the object finally hits the ground? Round to the nearest tenth of a second if necessary.

Accepted Answer

A)  2 seconds 
B)  $10.2$ seconds 
C)  5 seconds 
D)  $0.2$ seconds 
A)  2 seconds 
B)  $10.2$ seconds 
C)  5 seconds 
D)  $0.2$ seconds

Question 16

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the
x-axis or touches the x-axis and turns around, at each zero.
-$$f ( x ) = x ^ { 3 } + x ^ { 2 } - 20 x$$

Accepted Answer

A)  0 , multiplicity 1 , crosses the $x$-axis
- 5, multiplicity 1 , crosses the $x$-axis
4, multiplicity 1 , crosses the $x$-axis 
B)  0 , multiplicity 1 , crosses the $x$-axis
5 , multiplicity 1 , crosses the $x$-axis
$- 4$, multiplicity 1 , crosses the $x$-axis 
C)  0 , multiplicity 1 , touches the $x$-axis and turns around;
- 5, multiplicity 1 , touches the $x$-axis and turns around;
4 , multiplicity 1 , touches the $x$-axis and turns around 
D)  $- 5$, multiplicity 2 , touches the $x$-axis and turns around 4 , multiplicity 1 , crosses the $x$-axis 
A)  0 , multiplicity 1 , crosses the $x$-axis
- 5, multiplicity 1 , crosses the $x$-axis
4, multiplicity 1 , crosses the $x$-axis 
B)  0 , multiplicity 1 , crosses the $x$-axis
5 , multiplicity 1 , crosses the $x$-axis
$- 4$, multiplicity 1 , crosses the $x$-axis 
C)  0 , multiplicity 1 , touches the $x$-axis and turns around;
- 5, multiplicity 1 , touches the $x$-axis and turns around;
4 , multiplicity 1 , touches the $x$-axis and turns around 
D)  $- 5$, multiplicity 2 , touches the $x$-axis and turns around 4 , multiplicity 1 , crosses the $x$-axis

Question 17

Find the y-intercept for the graph of the quadratic function.
-$$f ( x ) = 6 + 5 x + x ^ { 2 }$$

Accepted Answer

A)  $( 0,3 )$ 
B)  $( 0 , - 6 )$ 
C)  $( 0,6 )$ 
D)  $( 0,5 )$ 
A)  $( 0,3 )$ 
B)  $( 0 , - 6 )$ 
C)  $( 0,6 )$ 
D)  $( 0,5 )$

Question 18

Solve the problem
-April shoots an arrow upward into the air at a speed of 64 feet per second from a platform that is 21 feet high. The height of the arrow is given by the function $h ( t ) = - 16 t ^ { 2 } + 64 t + 21$, where $t$ is the time is seconds. What is the maximum height of the arrow?

Accepted Answer

A)  $85 \mathrm { ft }$ 
B)  $21 \mathrm { ft }$ 
C)  $17 \mathrm { ft }$ 
D)  $64 \mathrm { ft }$ 
A)  $85 \mathrm { ft }$ 
B)  $21 \mathrm { ft }$ 
C)  $17 \mathrm { ft }$ 
D)  $64 \mathrm { ft }$

Question 19

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = ( x + 3 ) ^ { 2 } + 8$$

Accepted Answer

A)  $( 8 , - 9 )$ 
B)  $( - 3,8 )$ 
C)  $( - 8,3 )$ 
D)  $( 8 , - 3 )$ 
A)  $( 8 , - 9 )$ 
B)  $( - 3,8 )$ 
C)  $( - 8,3 )$ 
D)  $( 8 , - 3 )$

Question 20

Use the vertex and intercepts to sketch the graph of the quadratic function.
-$f ( x ) = 8 - x ^ { 2 } - 2 x$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Determine whether the graph shown is the graph of a polynomial function. -

Find the degree of the polynomial function. - $f ( x ) = 5 x - x ^ { 4 } + \frac { 5 } { 4 }$

Solve the problem. -Write an equation in standard form of the parabola that has the same shape as the graph of $f ( x ) = 5 x ^ { 2 }$ , but which has a minimum of 6 at $x = 2$ .

Find the range of the quadratic function. - $f ( x ) = - x ^ { 2 } - 14 x + 8$

Solve the problem -You have 120 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area.

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = x ^ { 2 } + 5 x - 6$

Solve the problem -A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 600 feet of fencing is used. Find the maximum area of the playground.

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = 3 ( x + 2 ) ( x + 5 ) ^ { 2 }$

Find the y-intercept of the polynomial function. - $f ( x ) = ( x + 1 ) ( x - 9 ) ( x - 1 ) ^ { 2 }$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. - $f ( x ) = - 3 x ^ { 2 } + 3 x - 3$

Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = ( x + 5 ) ^ { 2 } + 6$ $Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = ( x + 5 ) ^ { 2 } + 6$

Find the range of the quadratic function. - $f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 9$

Find the range of the quadratic function. - $y + 4 = ( x + 2 ) ^ { 2 }$

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = x ^ { 3 } + x ^ { 2 } - 20 x$

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = 6 + 5 x + x ^ { 2 }$

Solve the problem -April shoots an arrow upward into the air at a speed of 64 feet per second from a platform that is 21 feet high. The height of the arrow is given by the function $h ( t ) = - 16 t ^ { 2 } + 64 t + 21$ , where $t$ is the time is seconds. What is the maximum height of the arrow?

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x + 3 ) ^ { 2 } + 8$

Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = 8 - x ^ { 2 } - 2 x$ $Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = 8 - x ^ { 2 } - 2 x$

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Exam 3: Polynomial and Rational Functions

Determine whether the graph shown is the graph of a polynomial function. -

Find the degree of the polynomial function. - f(x)=5x−x4+54f ( x ) = 5 x - x ^ { 4 } + \frac { 5 } { 4 }f(x)=5x−x4+45​

Solve the problem. -Write an equation in standard form of the parabola that has the same shape as the graph of f(x)=5x2f ( x ) = 5 x ^ { 2 }f(x)=5x2 , but which has a minimum of 6 at x=2x = 2x=2 .

Find the range of the quadratic function. - f(x)=−x2−14x+8f ( x ) = - x ^ { 2 } - 14 x + 8f(x)=−x2−14x+8

Solve the problem -You have 120 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area.

Find the y-intercept for the graph of the quadratic function. - f(x)=x2+5x−6f ( x ) = x ^ { 2 } + 5 x - 6f(x)=x2+5x−6

Solve the problem -A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 600 feet of fencing is used. Find the maximum area of the playground.

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - f(x)=3(x+2)(x+5)2f ( x ) = 3 ( x + 2 ) ( x + 5 ) ^ { 2 }f(x)=3(x+2)(x+5)2

Find the y-intercept of the polynomial function. - f(x)=(x+1)(x−9)(x−1)2f ( x ) = ( x + 1 ) ( x - 9 ) ( x - 1 ) ^ { 2 }f(x)=(x+1)(x−9)(x−1)2

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. - f(x)=−3x2+3x−3f ( x ) = - 3 x ^ { 2 } + 3 x - 3f(x)=−3x2+3x−3

Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=(x+5)2+6f ( x ) = ( x + 5 ) ^ { 2 } + 6f(x)=(x+5)2+6

Find the range of the quadratic function. - f(x)=−7(x−2)2−9f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 9f(x)=−7(x−2)2−9

Find the range of the quadratic function. - y+4=(x+2)2y + 4 = ( x + 2 ) ^ { 2 }y+4=(x+2)2

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - f(x)=x3+x2−20xf ( x ) = x ^ { 3 } + x ^ { 2 } - 20 xf(x)=x3+x2−20x

Find the y-intercept for the graph of the quadratic function. - f(x)=6+5x+x2f ( x ) = 6 + 5 x + x ^ { 2 }f(x)=6+5x+x2

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=(x+3)2+8f ( x ) = ( x + 3 ) ^ { 2 } + 8f(x)=(x+3)2+8

Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=8−x2−2xf ( x ) = 8 - x ^ { 2 } - 2 xf(x)=8−x2−2x