Algebra 2

1101 Pages·2006·79.7 MB·English

by  McGraw-Hill

i s e
nteractive tudent dition
Authors
Holliday (cid:127) Luchin (cid:127) Cuevas (cid:127) Carter
Marks (cid:127) Day (cid:127) Casey (cid:127) Hayek
About the Cover
On a clear day, visitors to the top of the Gateway Arch in St. Louis,
Missouri, can see up to thirty miles to the east or west. The Arch,
towering 630 feet (192 meters) above the banks of the Mississippi
River, commemorates the westward expansion of the United
States in the 19th century. It takes the shape of a catenary curve,
which can be approximated using a quadratic function. You will
study quadratic functions in Chapter 5.
About the Graphics
3-D Lissajous curve. Created with Mathematica.
A 3-D Lissajous figure is constructed as a tube around a
trigonometric space curve. The radius of the tube is made
proportional to the distance to the nearest self-intersection. For
more information and for programs to construct such graphics,
see: www.wolfram.com/r/textbook.
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Except
as permitted under the United States Copyright Act, no part of this publication may be
reproduced or distributed in any form or by any means, or stored in a database or
retrieval system, without prior permission of the publisher.
Send all inquiries to:
Glencoe/McGraw-Hill
8787 Orion Place
Columbus, OH 43240-4027
ISBN: 978-0-07-873830-2
MHID: 0-07-873830-X
Printed in the United States of America.
1 2 3 4 5 6 7 8 9 10 043/079 15 14 13 12 11 10 09 08 07 06
Contents
in Brief

Unit 1 First-Degree Equations and Inequalities
1 Equations and Inequalities
2 Linear Relations and Functions
3 Systems of Equations and Inequalities
4 Matrices
Unit 2 Quadratic, Polynomial, and Radical Equations
and Inequalities
5 Quadratic Functions and Inequalities
6 Polynomial Functions
7 Radical Equations and Inequalities
Unit 3 Advanced Functions and Relations
8 Rational Expressions and Equations
9 Exponential and Logarithmic Relations
10 Conic Sections
Unit 4 Discrete Mathematics
11 Sequences and Series
12 Probability and Statistics
Unit 5 Trigonometry
13 Trigonometric Functions
14 Trigonometric Graphs and Identities
iii
Authors
Berchie Holliday, Ed.D. Gilbert J. Cuevas, Ph.D. Beatrice Luchin
National Mathematics Professor of Mathematics Mathematics Consultant
Consultant Education League City, TX
Silver Spring, MD University of Miami
Miami, FL
John A. Carter, Ph.D. Daniel Marks, Ed.D Roger Day, Ph.D.
Director of Mathematics Professor Emeritus of Mathematics Department
Adlai E. Stevenson High Mathematics Chairperson
School Auburn University at Pontiac Township High
Lincolnshire, IL Montgomery School
Mongomery, AL Pontiac, IL
iv
Ruth M. Casey Linda M. Hayek
Mathematics Teacher Mathematics Teacher
Department Chair Ralston Public Schools
Anderson County High Omaha, NE
School
Lawrenceburg, KY
Contributing Authors
Carol E. Malloy, Ph.D Viken Hovsepian Dinah Zike
Associate Professor Professor of Mathematics Educational Consultant,
University of North Carolina Rio Hondo College Dinah-Might Activities, Inc.
at Chapel Hill Whittier, CA San Antonio, TX
Chapel Hill, NC
Meet the Authors at algebra2.com v
Consultants
Glencoe/McGraw-Hill wishes to thank the following professionals for
their feedback. They were instrumental in providing valuable input
toward the development of this program in these specific areas.
Mathematical Content Graphing Calculator
Bob McCollum Ruth M. Casey
Associate Principal Mathematics Teacher
Curriculum and Instruction Department Chair
Glenbrook South High School Anderson County High School
Glenview, Illinois Lawrenceburg, Kentucky
Jerry Cummins
Differentiated Instruction
Former President
Nancy Frey, Ph.D. National Council of Supervisors of Mathematics
Associate Professor of Literacy Western Springs, Illinois
San Diego State University
San Diego, California Learning Disabilities
Kate Garnett, Ph.D.
English Language Learners
Chairperson, Coordinator Learning Disabilities
Mary Avalos, Ph.D. School of Education
Assistant Chair, Teaching and Learning Department of Special Education
Assistant Research Professor Hunter College, CUNY
University of Miami, School of Education New York, New York
Coral Gables, Florida
Mathematical Fluency
Jana Echevarria, Ph.D.
Professor, College of Education Jason Mutford
California State University, Long Beach Mathematics Instructor
Long Beach, California Coxsackie-Athens Central School District
Coxsackie, New York
Josefina V. Tinajero, Ph.D.
Dean, College of Educatifon
Pre-AP
The University of Texas at El Paso
El Paso, Texas Dixie Ross
AP Calculus Teacher
Gifted and Talented Pflugerville High School
Pflugerville, Texas
Ed Zaccaro
Author
Reading and Vocabulary
Mathematics and science books for gifted children
Bellevue, Iowa Douglas Fisher, Ph.D.
Director of Professional Development and Professor
City Heights Educational Collaborative
San Diego State University
San Diego, California
Lynn T. Havens
Director of Project CRISS
Kalispell School District
Kalispell, Montana
vi
Teacher Reviewers
Each Reviewer reviewed at least two chapters of the Student Edition, giving feedback
and suggestions for improving the effectiveness of the mathematics instruction.
Chrissy Aldridge Angela S. Davis M. Kathleen Kroh Tracey Shaw
Teacher Mathematics Teacher Mathematics Teacher Mathematics Teacher
Charlotte Latin School Bishop Spaugh Community Z. B. Vance High School Chatham Central High School
Charlotte, North Carolina Academy Charlotte, North Carolina Bear Creek, North Carolina
Charlotte, North Carolina
Harriette Neely Baker Tosha S. Lamar Marjorie Smith
Mathematics Teacher Sheri Dunn-Ulm Mathematics Instructor Mathematics Teacher
South Mecklenburg High School Teacher Phoenix High School Eastern Randolph High School
Charlotte, North Carolina Bainbridge High School Lawrenceville, Georgia Ramseur, North Carolina
Bainbridge, Georgia
Danny L. Barnes, NBCT Kay S. Laster McCoy Smith, III
Mathematics Teacher LaVonna M. Felton 8th Grade Pre-Algebra/ Mathematics Department Chair
Speight Middle School Mathematics Dept. Chair/8th Grade Algebra Teacher Sedgefield Middle School
Stantonsburg, North Carolina Lead Teacher Rockingham County Charlotte, North Carolina
James Martin Middle School Middle School
Aimee Barrette Bridget Sullivan
Charlotte, North Carolina Reidsville, North Carolina
Special Education Teacher 8th Grade Mathematics Teacher
Sedgefield Middle School Susan M. Fritsch Marcie Lebowitz Northeast Middle School
Charlotte, North Carolina Mathematics Teacher, NBCT Teacher Charlotte, North Carolina
David W. Butler High School Quail Hollow Middle School
Karen J. Blackert Marilyn R. Thompson
Matthews, North Carolina Charlotte, North Carolina
Mathematics Teacher Geometry/Mathematics Vertical
Myers Park High School Dr. Jesse R. Gassaway Joyce M. Lee Team Consultant
Charlotte, North Carolina Teacher Lead Mathematics Teacher Charlotte-Mecklenburg Schools
Northwest Guilford Middle School National Teachers Teaching with Charlotte, North Carolina
Patricia R. Blackwell
Greensboro, North Carolina Technology Instructor
Mathematics Department Chair Gwen Turner
George Washington Carver
East Mecklenburg High School Matt Gowdy Mathematics Teacher
High School
Charlotte, North Carolina Mathematics Teacher Clarke Central High School
Columbus, Georgia
Grimsley High School Athens, Georgia
Rebecca B. Caison
Greensboro, North Carolina Susan Marshall
Mathematics Teacher Elizabeth Webb
Mathematics Chairperson
Walter M. Williams High School Wendy Hancuff Mathematics Department Chair
Kernodle Middle School
Burlington, North Carolina Teacher Myers Park High School
Greensboro, North Carolina
Jack Britt High School Charlotte, North Carolina
Myra Cannon
Fayetteville, North Carolina Alice D. McLean
Mathematics Department Chair Jack Whittemore
Mathematics Coach
East Davidson High School Ernest A. Hoke Jr. C & I Resource Teacher
West Charlotte High School
Thomasville, North Carolina Mathematics Teacher Charlotte-Mecklenburg Schools
Charlotte, North Carolina
E. B. Aycock Middle School Charlotte, North Carolina
Peter K. Christensen
Greenville, North Carolina Portia Mouton
Mathematics/AP Teacher Angela Whittington
Mathematics Teacher
Central High School Carol B. Huss Mathematics Teacher
Westside High School
Macon, Georgia Mathematics Teacher North Forsyth High School
Macon, Georgia
Independence High School Winston-Salem, North Carolina
Rebecca Claiborne
Charlotte, North Carolina Elaine Pappas
Mathematics Department
Mathematics Department Chair Kentucky Consultants
Chairperson Deborah Ivy
Cedar Shoals High School
George Washington Carver Mathematics Teacher Amy Adams Cash
Athens, Georgia
High School Marie G. Davis Middle School Mathematics Educator/
Columbus, Georgia Charlotte, North Carolina Susan M. Peeples Department Chair
Laura Crook Lynda B. (Lucy) Kay Retired 8th Grade Mathematics Bowling Green High School
Mathematics Department Chair Mathematics Department Chair Teacher Bowling Green, Kentucky
Richland School District Two
Middle Creek High School Martin Middle School Susan Hack, NBCT
Columbia, South Carolina
Apex, North Carolina Raleigh, North Carolina Mathematics Teacher
Carolyn G. Randolph
Dayl F. Cutts Julia Kolb Oldham County High School
Teacher Mathematics Teacher/ Mathematics Department Chair Buckner, Kentucky
Kendrick High School
Northwest Guilford High School Department Chair Kimberly L. Henderson
Columbus, Georgia
Greensboro, North Carolina Leesville Road High School Hockney
Raleigh, North Carolina Mathematics Educator
Larry A. Ryle High School
Union, Kentucky
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Unit 1
CC HH AAPPTTEERR Equations and Inequalities
11
1-1 Expressions and Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1-2 Properties of Real Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1-3 Solving Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1-4 Solving Absolute Value Equations . . . . . . . . . . . . . . . . . . . . . . . . 27
Mid-Chapter Quiz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32
1-5 Solving Inequalities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Reading Math: Interval Notation. . . . . . . . . . . . . . . . . . . . . . . . .40
1-6 Solving Compound and Absolute Value Inequalities. . . . . . . . . 41
ASSESSMENT
Study Guide and Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49
Practice Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53
Standardized Test Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54
Prerequisite Skills
(cid:127) Get Ready for Chapter 1 5
(cid:127) Get Ready for the Next Lesson
10, 17, 26, 31, 39
Reading and Writing Mathematics
(cid:127) Reading Math 40
(cid:127) Vocabulary Link 19, 41, 42
(cid:127) Writing in Math 10, 17, 26, 31,
39, 47
(cid:127) Reading Math Tips 12, 35, 43
Standardized Test Practice
(cid:127) Multiple Choice 10, 17, 21, 23, 26,
31, 32, 39, 48, 53, 54, 55
H.O.T. Problems
Higher Order Thinking
(cid:127) Challenge 10, 17, 26, 31, 38, 47
(cid:127) Find the Error 25, 47
(cid:127) Open Ended 10, 17, 26, 30, 38, 47
(cid:127) Reasoning 10, 17, 26, 38
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Rudi Von Briel/PhotoEdit
C H APTER
2 Linear Relations and Functions
2-1 Relations and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Reading Math: Discrete and Continuous Functions in the
Real World. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
2-2 Linear Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66
2-3 Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Extend 2-3 Graphing Calculator Lab: The Family of
Linear Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78
2-4 Writing Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79
Mid-Chapter Quiz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .85
2-5 Statistics: Using Scatter Plots. . . . . . . . . . . . . . . . . . . . . . . . . . . .86
Extend 2-5 Graphing Calculator Lab: Lines of Regression . . . . .92
2-6 Special Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95
2-7 Graphing Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102
ASSESSMENT T
a
b
Study Guide and Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .106 l
e

o
Practice Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 f

C
Standardized Test Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 o
n
Prerequisite Skills te
n
(cid:127) Get Ready for Chapter 2 57 t
s
(cid:127) Get Ready for the Next Lesson
64, 70, 77, 84, 91, 101
Reading and Writing Mathematics
(cid:127) Reading Math 65
(cid:127) Writing in Math 64, 70, 76, 84, 91,
101, 105
(cid:127) Reading Math Tips 61, 74, 87
Standardized Test Practice
(cid:127) Multiple Choice 64, 70, 77, 82, 84,
85, 91, 101, 105, 111, 112, 113
(cid:127) Worked Out Example 80
H.O.T. Problems
Higher Order Thinking
(cid:127) Challenge 64, 70, 76, 84, 90, 100,
105
(cid:127) Find the Error 64, 76
(cid:127) Open Ended 64, 70, 76, 84, 91, 100
(cid:127) Reasoning 70, 76, 84, 100, 105
ix