Question 1

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

Accepted Answer

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

Question 2

Solve the problem
-A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 332 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?

Accepted Answer

A)  $27,556 \mathrm { ft } ^ { 2 }$ 
B)  $13,778 \mathrm { ft } ^ { 2 }$ 
C)  $20,667 \mathrm { ft } ^ { 2 }$ 
D)  $6889 \mathrm { ft } ^ { 2 }$ 
A)  $27,556 \mathrm { ft } ^ { 2 }$ 
B)  $13,778 \mathrm { ft } ^ { 2 }$ 
C)  $20,667 \mathrm { ft } ^ { 2 }$ 
D)  $6889 \mathrm { ft } ^ { 2 }$

Question 3

Use the vertex and intercepts to sketch the graph of the quadratic function.
-$f ( x ) = 3 ( x - 2 ) ^ { 2 } - 6$

Accepted Answer

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

Question 4

Solve the problem
-You have 240 feet of fencing to enclose a rectangular region. What is the maximum area?

Accepted Answer

A) 14,400 square feet 
B) 3600 square feet 
C) 3596 square feet 
D) 57,600 square feet 
A) 14,400 square feet 
B) 3600 square feet 
C) 3596 square feet 
D) 57,600 square feet

Question 5

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 6$$

Accepted Answer

A)  $( - 2 , - 6 )$ 
B)  $( - 6,2 )$ 
C)  $( 2 , - 6 )$ 
D)  $( - 7 , - 2 )$ 
A)  $( - 2 , - 6 )$ 
B)  $( - 6,2 )$ 
C)  $( 2 , - 6 )$ 
D)  $( - 7 , - 2 )$

Question 6

Find the axis of symmetry of the parabola defined by the given quadratic function.
-$$f ( x ) = ( x + 8 ) ^ { 2 } - 1$$

Accepted Answer

A)  $x = - 8$ 
B)  $x = 1$ 
C)  $x = 8$ 
D)  $x = - 1$ 
A)  $x = - 8$ 
B)  $x = 1$ 
C)  $x = 8$ 
D)  $x = - 1$

Question 7

Determine the maximum possible number of turning points for the graph of the function.
-$$f ( x ) = 5 x ^ { 8 } - 8 x ^ { 7 } - 9 x - 25$$

Accepted Answer

A)  8 
B)  5 
C)  0 
D)  7 
A)  8 
B)  5 
C)  0 
D)  7

Question 8

Use the Leading Coefficient Test to determine the end behavior of the polynomial function.
-$$f ( x ) = - 4 x ^ { 4 } + 3 x ^ { 3 } + 5 x ^ { 2 } - 2 x + 2$$

Accepted Answer

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

Question 9

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

Question 10

Use the Leading Coefficient Test to determine the end behavior of the polynomial function.
-$$f ( x ) = 2 x ^ { 3 } + 5 x ^ { 2 } + 5 x + 5$$

Accepted Answer

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

Question 11

Use the Leading Coefficient Test to determine the end behavior of the polynomial function.
-$$f ( x ) = - 5 \left( x ^ { 2 } - 5 \right) ( x - 3 ) ^ { 2 }$$

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Find the range of the quadratic function.
-$$f ( x ) = 11 ( x - 2 ) ^ { 2 } + 7$$

Accepted Answer

A)  $( - \infty , 7 ]$ 
B)  $[ 7 , \infty )$ 
C)  $[ - 7 , \infty )$ 
D)  $[ 2 , \infty )$ 
A)  $( - \infty , 7 ]$ 
B)  $[ 7 , \infty )$ 
C)  $[ - 7 , \infty )$ 
D)  $[ 2 , \infty )$

Question 14

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 15

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of
the minimum or maximum point.
-$$f ( x ) = 4 x ^ { 2 } - 12 x$$

Accepted Answer

A)  minimum; $\left( - \frac { 3 } { 2 } , - 9 \right)$ 
B)  maximum; $\left( \frac { 3 } { 2 } , - 9 \right)$ 
C)  minimum; $\left( \frac { 3 } { 2 } , - 9 \right)$ 
D)  maximum; $\left( - \frac { 3 } { 2 } , - 9 \right)$ 
A)  minimum; $\left( - \frac { 3 } { 2 } , - 9 \right)$ 
B)  maximum; $\left( \frac { 3 } { 2 } , - 9 \right)$ 
C)  minimum; $\left( \frac { 3 } { 2 } , - 9 \right)$ 
D)  maximum; $\left( - \frac { 3 } { 2 } , - 9 \right)$

Question 16

Determine whether the function is a polynomial function.
-$( x ) = 4 x ^ { 3 } + 3 x ^ { 2 } - 4 x ^ { - 5 } + 75$

Accepted Answer

A) No 
B) Yes 
A) No 
B) Yes

Question 17

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = x ^ { 2 } - 10 x - 7$$

Accepted Answer

A)  $( 5 , - 32 )$ 
B)  $( - 5,68 )$ 
C)  $( 5 , - 82 )$ 
D)  $( - 10,193 )$ 
A)  $( 5 , - 32 )$ 
B)  $( - 5,68 )$ 
C)  $( 5 , - 82 )$ 
D)  $( - 10,193 )$

Question 18

Find the y-intercept of the polynomial function.
-$$f ( x ) = - x ^ { 2 } + 2 x + 3$$

Accepted Answer

A)  $- 3$ 
B)  $- 1$ 
C)  0 
D)  3 
A)  $- 3$ 
B)  $- 1$ 
C)  0 
D)  3

Question 19

Find the zeros of the polynomial function
-$$f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 25 x$$

Accepted Answer

A)  $x = 1 , x = 5$ 
B)  $x = 0 , x = 5$ 
C)  $x = 0 , x = - 5$ 
D)  $x = 0 , x = - 5 , x = 5$ 
A)  $x = 1 , x = 5$ 
B)  $x = 0 , x = 5$ 
C)  $x = 0 , x = - 5$ 
D)  $x = 0 , x = - 5 , x = 5$

Question 20

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

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

Solve the problem -A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 332 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?

Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = 3 ( x - 2 ) ^ { 2 } - 6$ $Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = 3 ( x - 2 ) ^ { 2 } - 6$

Solve the problem -You have 240 feet of fencing to enclose a rectangular region. What is the maximum area?

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 6$

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = ( x + 8 ) ^ { 2 } - 1$

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = 5 x ^ { 8 } - 8 x ^ { 7 } - 9 x - 25$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - $f ( x ) = - 4 x ^ { 4 } + 3 x ^ { 3 } + 5 x ^ { 2 } - 2 x + 2$

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.

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - $f ( x ) = 2 x ^ { 3 } + 5 x ^ { 2 } + 5 x + 5$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - $f ( x ) = - 5 \left( x ^ { 2 } - 5 \right) ( x - 3 ) ^ { 2 }$

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

Find the range of the quadratic function. - $f ( x ) = 11 ( x - 2 ) ^ { 2 } + 7$

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

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. - $f ( x ) = 4 x ^ { 2 } - 12 x$

Determine whether the function is a polynomial function. - $( x ) = 4 x ^ { 3 } + 3 x ^ { 2 } - 4 x ^ { - 5 } + 75$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } - 10 x - 7$

Find the y-intercept of the polynomial function. - $f ( x ) = - x ^ { 2 } + 2 x + 3$

Find the zeros of the polynomial function - $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 25 x$

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

Equations and Inequalities

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Exponential and Logarithmic Functions

Systems of Equations and Inequalities

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Exam 3: Polynomial and Rational Functions

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

Solve the problem -A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 332 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?

Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=3(x−2)2−6f ( x ) = 3 ( x - 2 ) ^ { 2 } - 6f(x)=3(x−2)2−6

Solve the problem -You have 240 feet of fencing to enclose a rectangular region. What is the maximum area?

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=−7(x−2)2−6f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 6f(x)=−7(x−2)2−6

Find the axis of symmetry of the parabola defined by the given quadratic function. - f(x)=(x+8)2−1f ( x ) = ( x + 8 ) ^ { 2 } - 1f(x)=(x+8)2−1

Determine the maximum possible number of turning points for the graph of the function. - f(x)=5x8−8x7−9x−25f ( x ) = 5 x ^ { 8 } - 8 x ^ { 7 } - 9 x - 25f(x)=5x8−8x7−9x−25

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - f(x)=−4x4+3x3+5x2−2x+2f ( x ) = - 4 x ^ { 4 } + 3 x ^ { 3 } + 5 x ^ { 2 } - 2 x + 2f(x)=−4x4+3x3+5x2−2x+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.

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - f(x)=2x3+5x2+5x+5f ( x ) = 2 x ^ { 3 } + 5 x ^ { 2 } + 5 x + 5f(x)=2x3+5x2+5x+5

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - f(x)=−5(x2−5)(x−3)2f ( x ) = - 5 \left( x ^ { 2 } - 5 \right) ( x - 3 ) ^ { 2 }f(x)=−5(x2−5)(x−3)2

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

Find the range of the quadratic function. - f(x)=11(x−2)2+7f ( x ) = 11 ( x - 2 ) ^ { 2 } + 7f(x)=11(x−2)2+7

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

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)=4x2−12xf ( x ) = 4 x ^ { 2 } - 12 xf(x)=4x2−12x

Determine whether the function is a polynomial function. - (x)=4x3+3x2−4x−5+75( x ) = 4 x ^ { 3 } + 3 x ^ { 2 } - 4 x ^ { - 5 } + 75(x)=4x3+3x2−4x−5+75

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=x2−10x−7f ( x ) = x ^ { 2 } - 10 x - 7f(x)=x2−10x−7

Find the y-intercept of the polynomial function. - f(x)=−x2+2x+3f ( x ) = - x ^ { 2 } + 2 x + 3f(x)=−x2+2x+3

Find the zeros of the polynomial function - f(x)=x3−10x2+25xf ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 25 xf(x)=x3−10x2+25x

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

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Filters

Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = 3 ( x - 2 ) ^ { 2 } - 6$ $Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = 3 ( x - 2 ) ^ { 2 } - 6$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 6$

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = ( x + 8 ) ^ { 2 } - 1$

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = 5 x ^ { 8 } - 8 x ^ { 7 } - 9 x - 25$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - $f ( x ) = - 4 x ^ { 4 } + 3 x ^ { 3 } + 5 x ^ { 2 } - 2 x + 2$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - $f ( x ) = 2 x ^ { 3 } + 5 x ^ { 2 } + 5 x + 5$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - $f ( x ) = - 5 \left( x ^ { 2 } - 5 \right) ( x - 3 ) ^ { 2 }$

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

Find the range of the quadratic function. - $f ( x ) = 11 ( x - 2 ) ^ { 2 } + 7$

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. - $f ( x ) = 4 x ^ { 2 } - 12 x$

Determine whether the function is a polynomial function. - $( x ) = 4 x ^ { 3 } + 3 x ^ { 2 } - 4 x ^ { - 5 } + 75$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } - 10 x - 7$

Find the y-intercept of the polynomial function. - $f ( x ) = - x ^ { 2 } + 2 x + 3$

Find the zeros of the polynomial function - $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 25 x$