Dugopolski’s 37College Algebra
Chapter 3 Test — Form A Name:_________________________
Solve each problem.
1. Write in the form . Identify the vertex, axis of
symmetry, -intercept, -intercepts, and range. Sketch the graph.
Vertex form: ______________________
vertex: ________________
axis of symmetry: ________
y-intercept: ____________
x-intercepts: ____________
range: _________________
2. What is the remainder when is divided by ?
2. ______________________
3. Factor completely: .
3. ______________________
4. Find a polynomial equation with integral coefficients and lowest degree that has the roots
2 and 2 .
4. ______________________
5. Find all real and imaginary roots for the polynomial equation
5. ______________________
6. The altitude in feet of a projectile seconds after launch is given by the function
. Find the maximum altitude reached by the projectile.
6. ______________________
38 Form 3A
7. Solve the inequality: . State the solution using interval notation.
7. ______________________
8. Give the equations of all asymptotes for the graph of the function .
8. ______________________
Find all of the real and imaginary roots of each equation, stating multiplicity when it is
greater than one.
9. 10.
9. ______________________ 10. ______________________
Sketch the graph of each function.
11. 12. =
13. Solve the inequality: . State the solution using interval notation.
13. ______________________
Dugopolski’s 39College Algebra
Chapter 3 Test — Form B Name:_________________________
Solve each problem.
1. Write in the form . Identify the vertex, axis of
symmetry, -intercept, -intercepts, and range. Sketch the graph.
Vertex form: ______________________
vertex: ________________
axis of symmetry: ________
y-intercept: ____________
x-intercepts: ____________
range: _________________
2. What is the remainder when 3 1 is divided by ?
3 4 2
2. ______________________
3. Factor completely: .
3. ______________________
4. Find a polynomial equation with integral coefficients and lowest degree that has the roots
and .
4. ______________________
5. Find all real and imaginary roots for the polynomial equation
5. ______________________
6. The altitude in feet of a projectile seconds after launch is given by the function
. Find the maximum altitude reached by the projectile.
6. ______________________
40 Form 3B
7. Solve the inequality: . State the solution using interval notation.
7. ______________________
8. Give the equations of all asymptotes for the graph of the function .
3 5 2
8. ______________________
Find all of the real and imaginary roots of each equation, stating multiplicity when it is
greater than one.
9. 10.
9. ______________________ 10. ______________________
Sketch the graph of each function.
11. 12. =
13. Solve the inequality: . State the solution using interval notation.
13. ______________________
Dugopolski’s 41College Algebra
Chapter 3 Test — Form C Name:_________________________
Solve each problem.
1. What is the minimum value of in the function ?
1. ______________________
2. Is a factor of ? Show work to support your answer.
3
2. ______________________
3. Write the equation of a parabola that has vertex and -intercept
3. ______________________
4. Find a polynomial equation with real coefficients and lowest degree that has the roots
(with a multiplicity of 3), and .
4. ______________________
5. The altitude in feet of a projectile seconds after launch is given by the function
. Find the maximum altitude reached by the projectile.
5. ______________________
6. Use Descartes Rule of Signs to discuss the possibilities for the roots of
.
6. ______________________
42 Form 3C
7. Give the equations of all asymptotes for the graph of the function 2 .
7. ______________________
8. Solve the inequality: . State the solution using interval notation.
8. ______________________
9. Solve the inequalilty: . State the solution using interval notation.
9. ______________________
Find all of the real and imaginary roots of each equation, stating multiplicity when it is
greater than one.
10. 11.
3
10. ______________________ 11. ______________________
Sketch the graph of each function.
12. 13. =
Dugopolski’s 43College Algebra
Chapter 3 Test — Form D Name:_________________________
Solve each problem.
1. What is the minimum value of in the function ?
1. ______________________
2. Is a factor of ? Show work to support your answer.
3
2. ______________________
3. Write the equation of the parabola that has vertex and -intercept .
3. ______________________
4. Find a polynomial equation with real coefficients and lowest degree that has the roots
(with a multiplicity of 2), and .
4. ______________________
5. The altitude in feet of a projectile seconds after launch is given by the function
. Find the maximum altitude reached by the projectile.
5. ______________________
6. Use Descartes Rule of Signs to discuss the possibilities for the roots of
.
6. ______________________
44 Form 3D
7. Give the equations of all asymptotes for the graph of the function 2 .
7. ______________________
8. Solve the inequality: State the solution using interval notation.
8. ______________________
9. Solve the inequality: State the solution using interval notation.
9. ______________________
Find all of the real and imaginary roots of each equation, stating multiplicity when it is
greater than one.
10. 11. 3
10. ______________________ 11. ______________________
Sketch the graph of each function.
12. 13. =
Dugopolski’s 45College Algebra
Chapter 3 Test — Form 3E Name: _________________________
Multiple Choice: Choose the best answer for each of the following.
_____ 1. Find the -intercepts of the graph of .
a. c.
b d.
_____ 2. Find the axis of symmetry for
a. b. c. d.
_____ 3. Solve the inequality: .
a. c.
b. d.
_____ 4. What is the maximum value of in the function ?
a. b. c. d.
_____ 5. The altitude in feet of a projectile seconds after launch is given by the
function . How long after launch will it take for the
projectile to reach its maximum height ?
a. 1 sec. b. 2 sec. c. 2.5 sec. d. 4 sec.
_____ 6. Solve the inequality .
a. b. c. d.
_____ 7 Find all real and imaginary roots and state the multiplicity of a root when it is
greater than 1 for : .
a. (mult ), (mult ), c. , ,
b. , (mult ), d. , (mult ), (mult )
_____ 8. What is the remainder when is divided by
?
a. b. c. d.
_____ 9. Find a polynomial function with integral coefficients that has roots and .
a. c.
b. d.
46 Form 3E
_____ 10. Use the Theorem on Bounds to establish the best integral bounds for the roots
of
a. b. c. d. 2
_____ 11. Which of the following statements are true?
A. If , then as .
B. If (3, 9) and ( 3, 9) are both on the graph of , then the graph is
definitely symmetric to the -axis.
C. The graph of crosses the -axis when .
a. A and B b. B and C c. B only d. C only
_____ 12. Find the equation of a polynomial function with zeros of , multiplicity 2, and
, multiplicity 1.
a. c.
b. d.
_____ 13. Find all asymptotes for .
a. , c. ,
b. , d. ,
_____ 14. Find all vertical asymptotes for ( ) = .
a. = 1 b. = 1 c. = 1 d. None
_____ 15. Find the domain for ( ) .
a. { | } c. { | 0 and }
b. { | > } d. {all real numbers}
_____ 16. Solve the inequality:
a. c.
b d.
_____ 17. Find the vertex of the graph of the quadratic function:
.
a. b. c. d.
Dugopolski’s 47College Algebra
Chapter 3 Test — Form 3F Name:_________________________
Multiple Choice: Choose the best answer for each of the following.
_____ 1. Find the -intercepts for the graph of
a. c.
b. d.
_____ 2. Find the axis of symmetry for the graph of
a. b. c. d.
_____ 3. Solve the inequality: 8
a. c.
b. d.
_____ 4. What is the maximum value of in the function ?
a. b. c. d. 1
_____ 5. The altitude in feet of a projectile seconds after launch is given by the
function . How long after launch will it take for the
projectile to reach its maximum height ?
a. 1 sec. b. 2 sec. c. 2.5 sec. d. 3 sec.
_____ 6. Solve the inequality .
a. b. c. d.
_____ 7 Find all real and imaginary roots and state the multiplicity of a root when it is
greater than 1 for : .
a. (mult ), , c. , ,
b. (mult ), (mult ), d. , (mult ), (mult )
_____ 8. What is the remainder when is divided by
?
a. b. c. d.
_____ 9. Find a polynomial function with integral coefficients that has roots and .
a. c.
b. d.
48 Form 3F
_____ 10. Use the Theorem on Bounds to establish the best integral bounds for the roots
of
a. c.
b. d.
_____ 11. Which of the following statements are true?
A. If , then as .
B. If (3, 9) and ( 3, 9) are both on the graph of , then the graph is
definitely symmetric to the -axis.
C. The graph of crosses the -axis when .
a. C only b. A and C c. B only d. B and C
_____ 12. Find the equation of a polynomial function with zeros of , multiplicity ,
and , multiplicity .
a. c.
b. d.
_____ 13. Find all asymptotes for .
a. , c. ,
b. d. ,
_____ 14. Find all vertical asymptotes for ( ) = .
a. b. c. d. None
_____ 15. Find the domain for ( ) .
a. { | } c. { | 0 and }
b. { | > } d. {all real numbers}
_____ 16. Solve the inequality
a. c.
b d.
_____ 17. Find the vertex of the graph of the quadratic function:
a. b. c. d.
Dugopolski’s 117College Algebra
Chapter Test Keys
CHAPTER 3
118 Chapter 3 Test Key