Question 1

Find the standard form of the quadratic function shown below:

Accepted Answer

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

Question 2

Describe the right-hand and the left-hand behavior of the graph of   .

Accepted Answer

A)  Because the degree is even and the leading coefficient is negative, the graph falls to the left and rises to the right. 
B)  Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right. 
C)  Because the degree is even and the leading coefficient is negative, the graph falls to the left and falls to the right. 
D)  Because the degree is odd and the leading coefficient is negative, the graph rises to the left and rises to the right. 
E)  Because the degree is even and the leading coefficient is negative, the graph rises to the left and rises to the right. 
A)  Because the degree is even and the leading coefficient is negative, the graph falls to the left and rises to the right. 
B)  Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right. 
C)  Because the degree is even and the leading coefficient is negative, the graph falls to the left and falls to the right. 
D)  Because the degree is odd and the leading coefficient is negative, the graph rises to the left and rises to the right. 
E)  Because the degree is even and the leading coefficient is negative, the graph rises to the left and rises to the right.

Question 3

An open box is to be made from a square piece of cardboard, 32 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). If the volume of the box is represented by   , determine the domain of   .

Accepted Answer

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

Question 4

Write the standard form of the equation of the parabola that has a vertex at   and passes through the point   .

Accepted Answer

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

Question 5

The height,   , of a punted rugby ball is given by   where x is the horizontal distance in feet from the point where the ball is punted. How far, horizontally, is the ball from the kicker when it is at its highest point?

Accepted Answer

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

Question 6

Given   is a root, determine all other roots of   .

Accepted Answer

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E)

Question 7

Find all the real zeros of   .

Accepted Answer

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E)

Question 8

Use the zero or root feature of a graphing utility to approximate the zeros of   accurate to the nearest thousandth.

Accepted Answer

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

Question 9

A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below. If the perimeter of the window is   , express the area, A, as a function of the width, x, of the window.

Accepted Answer

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

Question 10

Find all real zeros of the polynomial   and determine the multiplicity of each.

Accepted Answer

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

Question 11

Find all zeros of the function   .

Accepted Answer

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

Question 12

Determine the vertex of the graph of the quadratic function   .

Accepted Answer

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D)    
E)

Question 13

After determining whether the variation model below is of the form   or   , find the value of k.

Accepted Answer

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

Question 14

Describe the right-hand and the left-hand behavior of the graph of   .

Accepted Answer

A)  Because the degree is odd and the leading coefficient is positive, the graph falls to the left and rises to the right. 
B)  Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right. 
C)  Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right. 
D)  Because the degree is odd and the leading coefficient is positive, the graph rises to the left and falls to the right. 
E)  Because the degree is even and the leading coefficient is positive, the graph rises to the left and rises to the right. 
A)  Because the degree is odd and the leading coefficient is positive, the graph falls to the left and rises to the right. 
B)  Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right. 
C)  Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right. 
D)  Because the degree is odd and the leading coefficient is positive, the graph rises to the left and falls to the right. 
E)  Because the degree is even and the leading coefficient is positive, the graph rises to the left and rises to the right.

Question 15

A farmer has 336 feet of fencing and wants to build two identical pens for his prize-winning pigs. The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area.

Accepted Answer

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

Question 16

Compare the graph of   with   .

Accepted Answer

A)    shifts left 7 units, shifts downward 5 units, and stretches by a factor of 9. 
B)    shifts left 7 units, shifts upward 5 units, and stretches by a factor of 9. 
C)    shifts right 7 units, shifts downward 5 units, and shrinks by a factor of  
) 
D)    shifts right 7 units, shifts upward 5 units, and shrinks by a factor of  
) 
E)    shifts right 7 units, shifts upward 5 units, and stretches by a factor of 9. 
A)    shifts left 7 units, shifts downward 5 units, and stretches by a factor of 9. 
B)    shifts left 7 units, shifts upward 5 units, and stretches by a factor of 9. 
C)    shifts right 7 units, shifts downward 5 units, and shrinks by a factor of  
) 
D)    shifts right 7 units, shifts upward 5 units, and shrinks by a factor of  
) 
E)    shifts right 7 units, shifts upward 5 units, and stretches by a factor of 9.

Question 17

If   is a root of   , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Accepted Answer

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

Question 18

Using the factors   and   , find the remaining factor(s) of   and write the polynomial in fully factored form.

Accepted Answer

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

Question 19

Find all real zeros of the polynomial   and determine the multiplicity of each.

Accepted Answer

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

Question 20

Use synthetic division to divide.

Accepted Answer

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

Find the standard form of the quadratic function shown below:

Describe the right-hand and the left-hand behavior of the graph of .

An open box is to be made from a square piece of cardboard, 32 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). If the volume of the box is represented by , determine the domain of .

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

The height, , of a punted rugby ball is given by where x is the horizontal distance in feet from the point where the ball is punted. How far, horizontally, is the ball from the kicker when it is at its highest point?

Given is a root, determine all other roots of .

Find all the real zeros of .

Use the zero or root feature of a graphing utility to approximate the zeros of accurate to the nearest thousandth.

A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below. If the perimeter of the window is , express the area, A, as a function of the width, x, of the window.

Find all real zeros of the polynomial and determine the multiplicity of each.

Find all zeros of the function .

Determine the vertex of the graph of the quadratic function .

After determining whether the variation model below is of the form or , find the value of k.

Describe the right-hand and the left-hand behavior of the graph of .

A farmer has 336 feet of fencing and wants to build two identical pens for his prize-winning pigs. The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area.

Compare the graph of with .

If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.

Find all real zeros of the polynomial and determine the multiplicity of each.

Use synthetic division to divide.

Prerequisites

Equations, Inequalities, and Mathematical Modeling

Functions and Their Graphs

Rational Functions and Conics

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Filters

Exam 4: Polynomial Functions

Find the standard form of the quadratic function shown below:

Describe the right-hand and the left-hand behavior of the graph of .

An open box is to be made from a square piece of cardboard, 32 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). If the volume of the box is represented by , determine the domain of .

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

The height, , of a punted rugby ball is given by where x is the horizontal distance in feet from the point where the ball is punted. How far, horizontally, is the ball from the kicker when it is at its highest point?

Given is a root, determine all other roots of .

Find all the real zeros of .

Use the zero or root feature of a graphing utility to approximate the zeros of accurate to the nearest thousandth.

A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below. If the perimeter of the window is , express the area, A, as a function of the width, x, of the window.

Find all real zeros of the polynomial and determine the multiplicity of each.

Find all zeros of the function .

Determine the vertex of the graph of the quadratic function .

After determining whether the variation model below is of the form or , find the value of k.

Describe the right-hand and the left-hand behavior of the graph of .

A farmer has 336 feet of fencing and wants to build two identical pens for his prize-winning pigs. The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area.

Compare the graph of with .

If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.

Find all real zeros of the polynomial and determine the multiplicity of each.

Use synthetic division to divide.

Prerequisites

Equations, Inequalities, and Mathematical Modeling

Functions and Their Graphs

Rational Functions and Conics

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Filters