Question 1

Find the x-intercepts (if any) for the graph of the quadratic function.
-$$y + 1 = ( x - 1 ) ^ { 2 }$$

Accepted Answer

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

Question 2

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

Accepted Answer

A)  $x = - 1$ 
B)  $x = 2$ 
C)  $x = 1$ 
D)  $x = - 5$ 
A)  $x = - 1$ 
B)  $x = 2$ 
C)  $x = 1$ 
D)  $x = - 5$

Question 3

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of
the minimum or maximum point.
-$$f ( x ) = - x ^ { 2 } - 2 x - 8$$

Accepted Answer

A)  maximum; $( - 7 , - 1 )$ 
B)  maximum; $( - 1 , - 7 )$ 
C)  minimum; $( - 1 , - 7 )$ 
D)  minimum; $( - 7 , - 1 )$ 
A)  maximum; $( - 7 , - 1 )$ 
B)  maximum; $( - 1 , - 7 )$ 
C)  minimum; $( - 1 , - 7 )$ 
D)  minimum; $( - 7 , - 1 )$

Question 4

Find the axis of symmetry of the parabola defined by the given quadratic function.
-$$f ( x ) = 4 x ^ { 2 } - 8 x - 9$$

Accepted Answer

A)  $x = - 1$ 
B)  $x = - 13$ 
C)  $x = 2$ 
D)  $x = 1$ 
A)  $x = - 1$ 
B)  $x = - 13$ 
C)  $x = 2$ 
D)  $x = 1$

Question 5

Solve the problem
-A person standing close to the edge on top of a 128-foot building throws a baseball vertically upward. The quadratic function $s ( t ) = - 16 t ^ { 2 } + 64 t + 128$ models the ball's height above the ground, $s ( t )$, in feet, $t$ seconds after it was thrown. After how many seconds does the ball reach its maximum height? Round to the nearest tenth of a second if necessary.

Accepted Answer

A)  $1.5$ seconds 
B)  192 seconds 
C)  2 seconds 
D)  $5.5$ seconds 
A)  $1.5$ seconds 
B)  192 seconds 
C)  2 seconds 
D)  $5.5$ seconds

Question 6

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

Accepted Answer

A)  $[ 7 , \infty )$ 
B)  $( - \infty , 7 ]$ 
C)  $[ 0 , \infty )$ 
D)  $[ - 7 , \infty )$ 
A)  $[ 7 , \infty )$ 
B)  $( - \infty , 7 ]$ 
C)  $[ 0 , \infty )$ 
D)  $[ - 7 , \infty )$

Question 7

Find the degree of the polynomial function.
-$$f ( x ) = \pi x ^ { 4 } + 7 x ^ { 3 } + 3$$

Accepted Answer

A)  3 
B)  4 
C)  $\pi$ 
D)  1 
A)  3 
B)  4 
C)  $\pi$ 
D)  1

Question 8

Find the y-intercept of the polynomial function.
-$$f ( x ) = - x ^ { 2 } ( x + 3 ) ( x - 9 )$$

Accepted Answer

A)  $- 27$ 
B)  27 
C)  $- 9$ 
D)  0 
A)  $- 27$ 
B)  27 
C)  $- 9$ 
D)  0

Question 9

Determine whether the function is a polynomial function.
-$$f ( x ) = 5 x ^ { 7 } - x ^ { 4 } + \frac { 3 } { 2 } x$$

Accepted Answer

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

Question 10

Solve the problem
-In one U.S. city, the quadratic function $f ( x ) = 0.0042 x ^ { 2 } - 0.46 x + 36.44$ models the median, or average, age, $y$, 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)  1953,36 years old 
B)  1936,49 years old 
C)  $1955,23.8$ years old 
D)  1955,49 years old 
A)  1953,36 years old 
B)  1936,49 years old 
C)  $1955,23.8$ years old 
D)  1955,49 years old

Question 11

Solve.
-The profits (in millions)for a company for 8 years were as follows:

Which of the following polynomials is the best model for this data?

Accepted Answer

A)  $P ( x ) = - 0.03 x ^ { 4 } - 0.3 x ^ { 2 } + 1.3 x + 0.17$ 
B)  $P ( x ) = - 0.08 x ^ { 3 } + 7 x ^ { 2 } + 1.3 x - 0.18$ 
C)  $\mathrm { P } ( \mathrm { x } ) = 0.03 \mathrm { x } ^ { 3 } - 0.3 \mathrm { x } ^ { 2 } + 1.3 \mathrm { x } + 0.17$ 
D)  $P ( x ) = 0.05 x ^ { 2 } - 0.8 x + 6$ 
A)  $P ( x ) = - 0.03 x ^ { 4 } - 0.3 x ^ { 2 } + 1.3 x + 0.17$ 
B)  $P ( x ) = - 0.08 x ^ { 3 } + 7 x ^ { 2 } + 1.3 x - 0.18$ 
C)  $\mathrm { P } ( \mathrm { x } ) = 0.03 \mathrm { x } ^ { 3 } - 0.3 \mathrm { x } ^ { 2 } + 1.3 \mathrm { x } + 0.17$ 
D)  $P ( x ) = 0.05 x ^ { 2 } - 0.8 x + 6$

Question 12

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.
-$$f ( x ) = \frac { 1 } { 3 } x ^ { 4 } \left( x ^ { 2 } - 3 \right) ( x + 8 )$$

Accepted Answer

A)  0 , multiplicity 4 , touches $x$-axis and turns around;
 $- 8$, multiplicity 1 , crosses $x$-axis
3 , multiplicity 2 , touches $x$-axis and turns around 
B)  0 , multiplicity 4 , touches $x$-axis and turns around;
$- 8$, multiplicity 1 , crosses $x$-axis;
$\sqrt { 3 }$, multiplicity 1 , crosses $x$-axis;
$- \sqrt { 3 }$, multiplicity 1 , crosses $x$-axis 
C)  0 , multiplicity 4 , crosses $x$-axis;
$- 8$, multiplicity 1 , touches $x$-axis and turns around;
$\sqrt { 3 }$, multiplicity 1 , touches $x$-axis and turns around;
$- \sqrt { 3 }$, multiplicity 1 , touches $x$-axis and turns around 
D)  0 , multiplicity 4 , touches $x$-axis and turns around; $- 8$, multiplicity 1 , crosses $x$-axis 
A)  0 , multiplicity 4 , touches $x$-axis and turns around;
 $- 8$, multiplicity 1 , crosses $x$-axis
3 , multiplicity 2 , touches $x$-axis and turns around 
B)  0 , multiplicity 4 , touches $x$-axis and turns around;
$- 8$, multiplicity 1 , crosses $x$-axis;
$\sqrt { 3 }$, multiplicity 1 , crosses $x$-axis;
$- \sqrt { 3 }$, multiplicity 1 , crosses $x$-axis 
C)  0 , multiplicity 4 , crosses $x$-axis;
$- 8$, multiplicity 1 , touches $x$-axis and turns around;
$\sqrt { 3 }$, multiplicity 1 , touches $x$-axis and turns around;
$- \sqrt { 3 }$, multiplicity 1 , touches $x$-axis and turns around 
D)  0 , multiplicity 4 , touches $x$-axis and turns around; $- 8$, multiplicity 1 , crosses $x$-axis

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

A)  $- 24$ 
B)  0 
C)  24 
D)  $- 4$ 
A)  $- 24$ 
B)  0 
C)  24 
D)  $- 4$

Question 15

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 $C ( x ) = 2 x ^ { 2 } - 28 x + 740$, where $x$ is the number of videos rented daily. Find the lowest cost to the nearest dollar.

Accepted Answer

A)  $\$ 348$ 
B)  $\$ 544$ 
C)  $\$ 838$ 
D)  $\$ 642$ 
A)  $\$ 348$ 
B)  $\$ 544$ 
C)  $\$ 838$ 
D)  $\$ 642$

Question 16

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = 11 ( x - 4 ) ^ { 2 } + 5$$

Accepted Answer

A)  $( - 4,5 )$ 
B)  $( 11,4 )$ 
C)  $( 4,5 )$ 
D)  $( 5 , - 4 )$ 
A)  $( - 4,5 )$ 
B)  $( 11,4 )$ 
C)  $( 4,5 )$ 
D)  $( 5 , - 4 )$

Question 17

Determine the maximum possible number of turning points for the graph of the function.
-$$( x ) = - x ^ { 2 } - 8 x + 15$$

Accepted Answer

A)  3 
B)  2 
C)  0 
D)  1 
A)  3 
B)  2 
C)  0 
D)  1

Question 18

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

Accepted Answer

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

Question 19

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = - x ^ { 2 } + 8 x - 4$$

Accepted Answer

A)  $( 4,12 )$ 
B)  $( 8 , - 4 )$ 
C)  $( - 4 , - 20 )$ 
D)  $( - 4 , - 52 )$ 
A)  $( 4,12 )$ 
B)  $( 8 , - 4 )$ 
C)  $( - 4 , - 20 )$ 
D)  $( - 4 , - 52 )$

Question 20

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.
-$$( x ) = 2 x ^ { 4 } - 3 x ^ { 2 }$$

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 falls to the right
  
D)  falls to the left and rises 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 falls to the right
  
D)  falls to the left and rises to the right

Find the x-intercepts (if any) for the graph of the quadratic function. - $y + 1 = ( x - 1 ) ^ { 2 }$

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

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. - $f ( x ) = - x ^ { 2 } - 2 x - 8$

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = 4 x ^ { 2 } - 8 x - 9$

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

Find the degree of the polynomial function. - $f ( x ) = \pi x ^ { 4 } + 7 x ^ { 3 } + 3$

Find the y-intercept of the polynomial function. - $f ( x ) = - x ^ { 2 } ( x + 3 ) ( x - 9 )$

Determine whether the function is a polynomial function. - $f ( x ) = 5 x ^ { 7 } - x ^ { 4 } + \frac { 3 } { 2 } x$

Solve. -The profits (in millions)for a company for 8 years were as follows: Which of the following polynomials is the best model for this data?

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. - $f ( x ) = \frac { 1 } { 3 } x ^ { 4 } \left( x ^ { 2 } - 3 \right) ( x + 8 )$

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

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

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 $C ( x ) = 2 x ^ { 2 } - 28 x + 740$ , where $x$ is the number of videos rented daily. Find the lowest cost to the nearest dollar.

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 11 ( x - 4 ) ^ { 2 } + 5$

Determine the maximum possible number of turning points for the graph of the function. - $( x ) = - x ^ { 2 } - 8 x + 15$

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

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = - x ^ { 2 } + 8 x - 4$

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. - $( x ) = 2 x ^ { 4 } - 3 x ^ { 2 }$

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Exam 3: Polynomial and Rational Functions

Find the x-intercepts (if any) for the graph of the quadratic function. - y+1=(x−1)2y + 1 = ( x - 1 ) ^ { 2 }y+1=(x−1)2

Find the axis of symmetry of the parabola defined by the given quadratic function. - f(x)=−x2+2x−6f ( x ) = - x ^ { 2 } + 2 x - 6f(x)=−x2+2x−6

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−8f ( x ) = - x ^ { 2 } - 2 x - 8f(x)=−x2−2x−8

Find the axis of symmetry of the parabola defined by the given quadratic function. - f(x)=4x2−8x−9f ( x ) = 4 x ^ { 2 } - 8 x - 9f(x)=4x2−8x−9

Find the range of the quadratic function. - f(x)=x2+7f ( x ) = x ^ { 2 } + 7f(x)=x2+7

Find the degree of the polynomial function. - f(x)=πx4+7x3+3f ( x ) = \pi x ^ { 4 } + 7 x ^ { 3 } + 3f(x)=πx4+7x3+3

Find the y-intercept of the polynomial function. - f(x)=−x2(x+3)(x−9)f ( x ) = - x ^ { 2 } ( x + 3 ) ( x - 9 )f(x)=−x2(x+3)(x−9)

Determine whether the function is a polynomial function. - f(x)=5x7−x4+32xf ( x ) = 5 x ^ { 7 } - x ^ { 4 } + \frac { 3 } { 2 } xf(x)=5x7−x4+23​x