Question 1

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

Accepted Answer

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

Question 2

Find the range of the quadratic function.
-$$f ( x ) = x ^ { 2 } - 10 x - 3$$

Accepted Answer

A)  $[ - 28 , \infty )$ 
B)  $[ - 5 , \infty )$ 
C)  $( - \infty , - 28 ]$ 
D)  $( - \infty , - 78 ]$ 
A)  $[ - 28 , \infty )$ 
B)  $[ - 5 , \infty )$ 
C)  $( - \infty , - 28 ]$ 
D)  $( - \infty , - 78 ]$ A

Question 3

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 8$$

Accepted Answer

A)  $( 2 , - 8 )$ 
B)  $( - 8,2 )$ 
C)  $( - 2 , - 8 )$ 
D)  $( - 7 , - 2 )$ 
A)  $( 2 , - 8 )$ 
B)  $( - 8,2 )$ 
C)  $( - 2 , - 8 )$ 
D)  $( - 7 , - 2 )$ A

Question 4

Find the domain and range of the quadratic function whose graph is described.
-The vertex is $( - 1 , - 5 )$ and the graph opens up.

Accepted Answer

A)  Domain: $( - \infty , \infty )$
Range: $[ - 5 , \infty )$ 
B)  Domain: $[ - 1 , \infty )$
Range: $[ - 5 , \infty )$ 
C)  Domain: $( - \infty , \infty )$
Range: $( - \infty , - 5 ]$ 
D)  Domain: $( - \infty , \infty )$
Range: $[ - 1 , \infty )$ 
A)  Domain: $( - \infty , \infty )$
Range: $[ - 5 , \infty )$ 
B)  Domain: $[ - 1 , \infty )$
Range: $[ - 5 , \infty )$ 
C)  Domain: $( - \infty , \infty )$
Range: $( - \infty , - 5 ]$ 
D)  Domain: $( - \infty , \infty )$
Range: $[ - 1 , \infty )$

Question 5

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

Accepted Answer

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

Question 6

Graph Parabolas
Use the vertex and intercepts to sketch the graph of the quadratic function.
-$$f ( x ) = - x ^ { 2 } - 2 x + 3$$

Accepted Answer

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

Question 7

Find the range of the quadratic function.
-$$f ( x ) = ( x + 5 ) ^ { 2 } + 9$$

Accepted Answer

A)  $[ 9 , \infty )$ 
B)  $[ - 9 , \infty )$ 
C)  $[ 5 , \infty )$ 
D)  $[ - 5 , \infty )$ [ 
A)  $[ 9 , \infty )$ 
B)  $[ - 9 , \infty )$ 
C)  $[ 5 , \infty )$ 
D)  $[ - 5 , \infty )$ [

Question 8

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. 768 feet of fencing is used. Find the maximum area of the playground.

Accepted Answer

A)  $24,576 \mathrm { ft } ^ { 2 }$ 
B)  $36,864 \mathrm { ft } ^ { 2 }$ 
C)  $18,432 \mathrm { ft } ^ { 2 }$ 
D)  $27,648 \mathrm { ft } ^ { 2 }$ 
A)  $24,576 \mathrm { ft } ^ { 2 }$ 
B)  $36,864 \mathrm { ft } ^ { 2 }$ 
C)  $18,432 \mathrm { ft } ^ { 2 }$ 
D)  $27,648 \mathrm { ft } ^ { 2 }$

Question 9

Find the domain and range of the quadratic function whose graph is described.
-The vertex is $( 1 , - 14 )$ and the graph opens down.

Accepted Answer

A)  Domain: $( - \infty , \infty )$
Range: $( - \infty , - 14 ]$ 
B)  Domain: $( - \infty , 1 ]$
Range: $( - \infty , - 14 ]$ 
C)  Domain: $( - \infty , \infty )$
Range: $[ - 14 , \infty )$ 
D)  Domain: $( - \infty , \infty )$
Range: $( - \infty , 1 ]$ 
A)  Domain: $( - \infty , \infty )$
Range: $( - \infty , - 14 ]$ 
B)  Domain: $( - \infty , 1 ]$
Range: $( - \infty , - 14 ]$ 
C)  Domain: $( - \infty , \infty )$
Range: $[ - 14 , \infty )$ 
D)  Domain: $( - \infty , \infty )$
Range: $( - \infty , 1 ]$

Question 10

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

Accepted Answer

A)  maximum; $( - 1 , - 3 )$ 
B)  minimum; $( - 1 , - 3 )$ 
C)  minimum; $( - 3 , - 1 )$ 
D)  maximum; $( - 3 , - 1 )$ 
A)  maximum; $( - 1 , - 3 )$ 
B)  minimum; $( - 1 , - 3 )$ 
C)  minimum; $( - 3 , - 1 )$ 
D)  maximum; $( - 3 , - 1 )$

Question 11

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

Accepted Answer

A)  $( - \infty , 6 ]$ 
B)  $[ 6 , \infty )$ 
C)  $( - \infty , 2 ]$ 
D)  $[ - 2 , \infty )$ 
A)  $( - \infty , 6 ]$ 
B)  $[ 6 , \infty )$ 
C)  $( - \infty , 2 ]$ 
D)  $[ - 2 , \infty )$

Question 12

Graph Parabolas
Use the vertex and intercepts to sketch the graph of the quadratic function.
-$$f ( x ) = - x ^ { 2 } + 6 x - 8$$

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Find the axis of symmetry of the parabola defined by the given quadratic function.
-$$f ( x ) = ( x + 4 ) ^ { 2 } + 9$$

Accepted Answer

A)  $x = - 4$ 
B)  $x = 4$ 
C)  $\mathrm { y } = 9$ 
D)  $y = - 9$ 
A)  $x = - 4$ 
B)  $x = 4$ 
C)  $\mathrm { y } = 9$ 
D)  $y = - 9$

Question 16

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = ( x + 4 ) ^ { 2 } + 9$$

Accepted Answer

A)  $( - 4,9 )$ 
B)  $( - 9,4 )$ 
C)  $( 9 , - 16 )$ 
D)  $( 9 , - 4 )$ 
A)  $( - 4,9 )$ 
B)  $( - 9,4 )$ 
C)  $( 9 , - 16 )$ 
D)  $( 9 , - 4 )$

Question 17

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$f ( x ) = - x ^ { 2 } - 4 x - 9$

Accepted Answer

A)  $( - 2 , - 5 )$ 
B)  $( 2 , - 21 )$ 
C)  $( - 4 , - 9 )$ 
D)  $( 2 , - 13 )$ 
A)  $( - 2 , - 5 )$ 
B)  $( 2 , - 21 )$ 
C)  $( - 4 , - 9 )$ 
D)  $( 2 , - 13 )$

Question 18

Find the x-intercepts (if any)for the graph of the quadratic function.
-$$f ( x ) = 2 x ^ { 2 } - 14 x + 24$$

Accepted Answer

A)  $( 4,0 )$ and $( 3,0 )$ 
B)  $( 4,0 )$ and $( - 3,0 )$ 
C)  $( 6,0 )$ and $( 2,0 )$ 
D)  $( 6,0 )$ and $( - 2,0 )$ 
A)  $( 4,0 )$ and $( 3,0 )$ 
B)  $( 4,0 )$ and $( - 3,0 )$ 
C)  $( 6,0 )$ and $( 2,0 )$ 
D)  $( 6,0 )$ and $( - 2,0 )$

Question 19

Find the y-intercept for the graph of the quadratic function.
-$$f ( x ) = - x ^ { 2 } - 2 x + 8$$

Accepted Answer

A)  $( 0,8 )$ 
B)  $( 8,0 )$ 
C)  $( 0 , - 4 )$ 
D)  $( 0 , - 8 )$ 
A)  $( 0,8 )$ 
B)  $( 8,0 )$ 
C)  $( 0 , - 4 )$ 
D)  $( 0 , - 8 )$

Question 20

Solve the problem.
-The profit that the vendor makes per day by selling $x$ pretzels is given by the function $P ( x ) = - 0.004 x ^ { 2 } + 2.4 x - 200$. Find the number of pretzels that must be sold to maximize profit.

Accepted Answer

A)  300 pretzels 
B)  600 pretzels 
C)  $1.2$ pretzels 
D)  160 pretzels 
A)  300 pretzels 
B)  600 pretzels 
C)  $1.2$ pretzels 
D)  160 pretzels

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

Find the range of the quadratic function. - $f ( x ) = x ^ { 2 } - 10 x - 3$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 8$

Find the domain and range of the quadratic function whose graph is described. -The vertex is $( - 1 , - 5 )$ and the graph opens up.

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

Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = - x ^ { 2 } - 2 x + 3$ $Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = - x ^ { 2 } - 2 x + 3$

Find the range of the quadratic function. - $f ( x ) = ( x + 5 ) ^ { 2 } + 9$

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. 768 feet of fencing is used. Find the maximum area of the playground.

Find the domain and range of the quadratic function whose graph is described. -The vertex is $( 1 , - 14 )$ and the graph opens down.

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

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

Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = - x ^ { 2 } + 6 x - 8$ $Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = - x ^ { 2 } + 6 x - 8$

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

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

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = ( x + 4 ) ^ { 2 } + 9$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x + 4 ) ^ { 2 } + 9$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = - x ^ { 2 } - 4 x - 9$

Find the x-intercepts (if any)for the graph of the quadratic function. - $f ( x ) = 2 x ^ { 2 } - 14 x + 24$

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = - x ^ { 2 } - 2 x + 8$

Solve the problem. -The profit that the vendor makes per day by selling $x$ pretzels is given by the function $P ( x ) = - 0.004 x ^ { 2 } + 2.4 x - 200$ . Find the number of pretzels that must be sold to maximize profit.

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Exam 3: Polynomial and Rational Functions

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

Find the range of the quadratic function. - f(x)=x2−10x−3f ( x ) = x ^ { 2 } - 10 x - 3f(x)=x2−10x−3

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=−7(x−2)2−8f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 8f(x)=−7(x−2)2−8

Find the domain and range of the quadratic function whose graph is described. -The vertex is (−1,−5)( - 1 , - 5 )(−1,−5) and the graph opens up.

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

Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=−x2−2x+3f ( x ) = - x ^ { 2 } - 2 x + 3f(x)=−x2−2x+3

Find the range of the quadratic function. - f(x)=(x+5)2+9f ( x ) = ( x + 5 ) ^ { 2 } + 9f(x)=(x+5)2+9

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. 768 feet of fencing is used. Find the maximum area of the playground.

Find the domain and range of the quadratic function whose graph is described. -The vertex is (1,−14)( 1 , - 14 )(1,−14) and the graph opens down.

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)=−x2−2x−4f ( x ) = - x ^ { 2 } - 2 x - 4f(x)=−x2−2x−4

Find the range of the quadratic function. - f(x)=6−(x+2)2f ( x ) = 6 - ( x + 2 ) ^ { 2 }f(x)=6−(x+2)2

Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=−x2+6x−8f ( x ) = - x ^ { 2 } + 6 x - 8f(x)=−x2+6x−8

Find the range of the quadratic function. - f(x)=−7(x−2)2−4f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 4f(x)=−7(x−2)2−4

Find the range of the quadratic function. - f(x)=(x+8)2−3f ( x ) = ( x + 8 ) ^ { 2 } - 3f(x)=(x+8)2−3

Find the axis of symmetry of the parabola defined by the given quadratic function. - f(x)=(x+4)2+9f ( x ) = ( x + 4 ) ^ { 2 } + 9f(x)=(x+4)2+9

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=(x+4)2+9f ( x ) = ( x + 4 ) ^ { 2 } + 9f(x)=(x+4)2+9

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=−x2−4x−9f ( x ) = - x ^ { 2 } - 4 x - 9f(x)=−x2−4x−9

Find the x-intercepts (if any)for the graph of the quadratic function. - f(x)=2x2−14x+24f ( x ) = 2 x ^ { 2 } - 14 x + 24f(x)=2x2−14x+24

Find the y-intercept for the graph of the quadratic function. - f(x)=−x2−2x+8f ( x ) = - x ^ { 2 } - 2 x + 8f(x)=−x2−2x+8

Solve the problem. -The profit that the vendor makes per day by selling xxx pretzels is given by the function P(x)=−0.004x2+2.4x−200P ( x ) = - 0.004 x ^ { 2 } + 2.4 x - 200P(x)=−0.004x2+2.4x−200 . Find the number of pretzels that must be sold to maximize profit.