Question 1

Find the y-intercept for the graph of the quadratic function.
-$$f ( x ) = 4 + 5 x + x ^ { 2 }$$

Accepted Answer

A)  $( 0,4 )$ 
B)  $( 0,1 )$ 
C)  $( 0 , - 4 )$ 
D)  $( 0,5 )$ 
A)  $( 0,4 )$ 
B)  $( 0,1 )$ 
C)  $( 0 , - 4 )$ 
D)  $( 0,5 )$

Question 2

Find the range of the quadratic function.
-$$f ( x ) = x ^ { 2 } + 5$$

Accepted Answer

A)  $[ 5 , \infty )$ 
B)  $( - \infty , 5 ]$ 
C)  $[ - 5 , \infty )$ 
D)  $[ 0 , \infty )$ 
A)  $[ 5 , \infty )$ 
B)  $( - \infty , 5 ]$ 
C)  $[ - 5 , \infty )$ 
D)  $[ 0 , \infty )$

Question 3

Solve the problem.
-Write an equation in standard form of the parabola that has the same shape as the graph of $f ( x ) = - 7 x ^ { 2 }$, but which has a maximum of 9 at $x = 2$.

Accepted Answer

A)  $f ( x ) = - 7 ( x - 2 ) ^ { 2 } + 9$ 
B)  $f ( x ) = - 7 ( x + 2 ) ^ { 2 } + 9$ 
C)  $f ( x ) = 7 ( x - 2 ) ^ { 2 } + 9$ 
D)  $f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 9$ 
A)  $f ( x ) = - 7 ( x - 2 ) ^ { 2 } + 9$ 
B)  $f ( x ) = - 7 ( x + 2 ) ^ { 2 } + 9$ 
C)  $f ( x ) = 7 ( x - 2 ) ^ { 2 } + 9$ 
D)  $f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 9$

Question 4

Find the x-intercepts (if any)for the graph of the quadratic function.
-$f ( x ) = 2 x ^ { 2 } - 30 x + 112$

Accepted Answer

A)  $( 8,0 )$ and $( 7,0 )$ 
B)  $( - 8,0 )$ and $( - 7,0 )$ 
C)  $( 8,0 )$ and $( - 7,0 )$ 
D)  $( - 8,0 )$ and $( 7,0 )$ 
A)  $( 8,0 )$ and $( 7,0 )$ 
B)  $( - 8,0 )$ and $( - 7,0 )$ 
C)  $( 8,0 )$ and $( - 7,0 )$ 
D)  $( - 8,0 )$ and $( 7,0 )$

Question 5

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 $C ( x ) = 2 x ^ { 2 } - 32 x + 730$, where $x$ is the number of videos rented daily. Find the lowest cost to the nearest dollar.

Accepted Answer

A)  $\$ 602$ 
B)  $\$ 218$ 
C)  $\$ 474$ 
D)  $\$ 858$ 
A)  $\$ 602$ 
B)  $\$ 218$ 
C)  $\$ 474$ 
D)  $\$ 858$

Question 6

The graph of a quadratic function is given. Determine the function's equation.
-

Accepted Answer

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

Question 7

Find the x-intercepts (if any)for the graph of the quadratic function.
-$f ( x ) = x ^ { 2 } + 16 x + 47$ Give your answers in exact form.

Accepted Answer

A)  $( - 8 \pm \sqrt { 17 } , 0 )$ 
B)  $( 8 + \sqrt { 17 } , 0 )$ 
C)  $( 8 \pm \sqrt { 47 } , 0 )$ 
D)  $( - 16 \pm \sqrt { 47 } , 0 )$ 
A)  $( - 8 \pm \sqrt { 17 } , 0 )$ 
B)  $( 8 + \sqrt { 17 } , 0 )$ 
C)  $( 8 \pm \sqrt { 47 } , 0 )$ 
D)  $( - 16 \pm \sqrt { 47 } , 0 )$

Question 8

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = x ^ { 2 } - 4$$

Accepted Answer

A)  $( 0 , - 4 )$ 
B)  $( 1,0 )$ 
C)  $( 0,4 )$ 
D)  $( 4,0 )$ 
A)  $( 0 , - 4 )$ 
B)  $( 1,0 )$ 
C)  $( 0,4 )$ 
D)  $( 4,0 )$

Question 9

Find the axis of symmetry of the parabola defined by the given quadratic function.
-$$f ( x ) = x ^ { 2 } + 14 x + 2$$

Accepted Answer

A)  $x = - 7$ 
B)  $x = 7$ 
C)  $x = 14$ 
D)  $x = - 47$ 
A)  $x = - 7$ 
B)  $x = 7$ 
C)  $x = 14$ 
D)  $x = - 47$

Question 10

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

Accepted Answer

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

Question 11

Solve the problem.
-A rain gutter is made from sheets of aluminum that are 18 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross-sectional area and allow the
Greatest amount of water to flow.

Accepted Answer

A) 4.5 inches 
B) 4 inches 
C) 5 inches 
D) 5.5 inches 
A) 4.5 inches 
B) 4 inches 
C) 5 inches 
D) 5.5 inches

Question 12

Graph Parabolas
Use the vertex and intercepts to sketch the graph of the quadratic function.
-$$f ( x ) = ( x + 4 ) ^ { 2 } - 1$$

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

Graph Parabolas
Use the vertex and intercepts to sketch the graph of the quadratic function.
-$$f ( x ) = 4 - ( x - 2 ) ^ { 2 }$$

Accepted Answer

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

Question 15

Find the axis of symmetry of the parabola defined by the given quadratic function.
-$$y + 9 = ( x + 3 ) ^ { 2 }$$

Accepted Answer

A)  $x = - 3$ 
B)  $x = 3$ 
C)  $y = 9$ 
D)  $\mathrm { y } = - 9$ y 
A)  $x = - 3$ 
B)  $x = 3$ 
C)  $y = 9$ 
D)  $\mathrm { y } = - 9$ y

Question 16

The graph of a quadratic function is given. Determine the function's equation.
-

Accepted Answer

A)  $j ( x ) = x ^ { 2 } + 3$ 
B)  $g ( x ) = x ^ { 2 } + 6 x + 9$ 
C)  $h ( x ) = x ^ { 2 } - 3$ 
D)  $f ( x ) = x ^ { 2 } - 6 x + 9$ 
A)  $j ( x ) = x ^ { 2 } + 3$ 
B)  $g ( x ) = x ^ { 2 } + 6 x + 9$ 
C)  $h ( x ) = x ^ { 2 } - 3$ 
D)  $f ( x ) = x ^ { 2 } - 6 x + 9$

Question 17

Solve the problem.
-In one U.S. city, the quadratic function $f ( x ) = 0.0036 x ^ { 2 } - 0.44 x + 36.95$ models the median, or average, age, $\mathrm { y }$, at which men were first married x years after 1900 . In which year was this average age at a minimum? (Round to the nearest year.) What was the average age at first marriage for that year? (Round to the nearest tenth.)

Accepted Answer

A)  $1961,23.5$ years old 
B)  $1961,50.4$ years old 
C)  $1936,50.4$ years old 
D)  1953,36 years old 
A)  $1961,23.5$ years old 
B)  $1961,50.4$ years old 
C)  $1936,50.4$ years old 
D)  1953,36 years old

Question 18

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

Accepted Answer

A)  $\left( - \infty , \frac { 3 } { 4 } \right]$ 
B)  $\left( - \infty , - \frac { 3 } { 4 } \right]$ 
C)  $\left( - \infty , - \frac { 1 } { 2 } \right]$ 
D)  $\left( - \infty , \frac { 1 } { 2 } \right]$ 
A)  $\left( - \infty , \frac { 3 } { 4 } \right]$ 
B)  $\left( - \infty , - \frac { 3 } { 4 } \right]$ 
C)  $\left( - \infty , - \frac { 1 } { 2 } \right]$ 
D)  $\left( - \infty , \frac { 1 } { 2 } \right]$

Question 19

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. 528 feet of fencing is used. Find the dimensions of the playground that maximize the
Total enclosed area.

Accepted Answer

A) 88 ft by 132 ft 
B) 132 ft by 132 ft 
C) 44 ft by 198 ft 
D) 66 ft by 132 ft 
A) 88 ft by 132 ft 
B) 132 ft by 132 ft 
C) 44 ft by 198 ft 
D) 66 ft by 132 ft

Question 20

Determine a Quadratic Function's Minimum or Maximum Value
Determine whether the given quadratic function has a minimum value or maximum value. Then find the
coordinates of the minimum or maximum point.
-$$f ( x ) = - 4 x ^ { 2 } + 4 x$$

Accepted Answer

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

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = 4 + 5 x + x ^ { 2 }$

Find the range of the quadratic function. - $f ( x ) = x ^ { 2 } + 5$

Solve the problem. -Write an equation in standard form of the parabola that has the same shape as the graph of $f ( x ) = - 7 x ^ { 2 }$ , but which has a maximum of 9 at $x = 2$ .

Find the x-intercepts (if any)for the graph of the quadratic function. - $f ( x ) = 2 x ^ { 2 } - 30 x + 112$

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 $C ( x ) = 2 x ^ { 2 } - 32 x + 730$ , where $x$ is the number of videos rented daily. Find the lowest cost to the nearest dollar.

The graph of a quadratic function is given. Determine the function's equation. -

Find the x-intercepts (if any)for the graph of the quadratic function. - $f ( x ) = x ^ { 2 } + 16 x + 47$ Give your answers in exact form.

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } - 4$

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 14 x + 2$

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

Solve the problem. -A rain gutter is made from sheets of aluminum that are 18 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross-sectional area and allow the Greatest amount of water to flow.

Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = ( x + 4 ) ^ { 2 } - 1$ $Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = ( x + 4 ) ^ { 2 } - 1$

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

Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = 4 - ( x - 2 ) ^ { 2 }$ $Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = 4 - ( x - 2 ) ^ { 2 }$

Find the axis of symmetry of the parabola defined by the given quadratic function. - $y + 9 = ( x + 3 ) ^ { 2 }$

The graph of a quadratic function is given. Determine the function's equation. -

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

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. 528 feet of fencing is used. Find the dimensions of the playground that maximize the Total enclosed area.

Determine a Quadratic Function's Minimum or Maximum Value Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. - $f ( x ) = - 4 x ^ { 2 } + 4 x$

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences, Induction, and Probability

Filters

Exam 3: Polynomial and Rational Functions

Find the y-intercept for the graph of the quadratic function. - f(x)=4+5x+x2f ( x ) = 4 + 5 x + x ^ { 2 }f(x)=4+5x+x2

Find the range of the quadratic function. - f(x)=x2+5f ( x ) = x ^ { 2 } + 5f(x)=x2+5

Solve the problem. -Write an equation in standard form of the parabola that has the same shape as the graph of f(x)=−7x2f ( x ) = - 7 x ^ { 2 }f(x)=−7x2 , but which has a maximum of 9 at x=2x = 2x=2 .

Find the x-intercepts (if any)for the graph of the quadratic function. - f(x)=2x2−30x+112f ( x ) = 2 x ^ { 2 } - 30 x + 112f(x)=2x2−30x+112

The graph of a quadratic function is given. Determine the function's equation. -

Find the x-intercepts (if any)for the graph of the quadratic function. - f(x)=x2+16x+47f ( x ) = x ^ { 2 } + 16 x + 47f(x)=x2+16x+47 Give your answers in exact form.

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=x2−4f ( x ) = x ^ { 2 } - 4f(x)=x2−4

Find the axis of symmetry of the parabola defined by the given quadratic function. - f(x)=x2+14x+2f ( x ) = x ^ { 2 } + 14 x + 2f(x)=x2+14x+2

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

Solve the problem. -A rain gutter is made from sheets of aluminum that are 18 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross-sectional area and allow the Greatest amount of water to flow.

Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=(x+4)2−1f ( x ) = ( x + 4 ) ^ { 2 } - 1f(x)=(x+4)2−1

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

Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=4−(x−2)2f ( x ) = 4 - ( x - 2 ) ^ { 2 }f(x)=4−(x−2)2

Find the axis of symmetry of the parabola defined by the given quadratic function. - y+9=(x+3)2y + 9 = ( x + 3 ) ^ { 2 }y+9=(x+3)2

The graph of a quadratic function is given. Determine the function's equation. -

Find the range of the quadratic function. - f(x)=−3x2−3xf ( x ) = - 3 x ^ { 2 } - 3 xf(x)=−3x2−3x

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. 528 feet of fencing is used. Find the dimensions of the playground that maximize the Total enclosed area.

Determine a Quadratic Function's Minimum or Maximum Value Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. - f(x)=−4x2+4xf ( x ) = - 4 x ^ { 2 } + 4 xf(x)=−4x2+4x

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences, Induction, and Probability

Filters

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = 4 + 5 x + x ^ { 2 }$

Find the range of the quadratic function. - $f ( x ) = x ^ { 2 } + 5$

Solve the problem. -Write an equation in standard form of the parabola that has the same shape as the graph of $f ( x ) = - 7 x ^ { 2 }$ , but which has a maximum of 9 at $x = 2$ .

Find the x-intercepts (if any)for the graph of the quadratic function. - $f ( x ) = 2 x ^ { 2 } - 30 x + 112$

Find the x-intercepts (if any)for the graph of the quadratic function. - $f ( x ) = x ^ { 2 } + 16 x + 47$ Give your answers in exact form.

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } - 4$

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 14 x + 2$

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

Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = ( x + 4 ) ^ { 2 } - 1$ $Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = ( x + 4 ) ^ { 2 } - 1$

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

Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = 4 - ( x - 2 ) ^ { 2 }$ $Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = 4 - ( x - 2 ) ^ { 2 }$

Find the axis of symmetry of the parabola defined by the given quadratic function. - $y + 9 = ( x + 3 ) ^ { 2 }$

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

Determine a Quadratic Function's Minimum or Maximum Value Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. - $f ( x ) = - 4 x ^ { 2 } + 4 x$