Cliff Notes - StudySolver Algebra II

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CliffsStudySolver™

Algebra II

By Mary Jane Sterling

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CliffsStudySolver™

Algebra II

By Mary Jane Sterling

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Published by:

Wiley Publishing, Inc.

111 River Street

Hoboken, NJ 07030-5774

www.wiley.com

Published by Wiley Publishing, Inc., New York, NY

Published simultaneously in Canada

ISBN: 0-7645-4135-8

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

1B/SW/QR/QU/IN

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by

any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted

under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permis-

sion of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright

Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-646-8600. Requests to

the Publisher for permission should be addressed to the Legal Department, Wiley Publishing, Inc., 10475

Crosspoint Blvd., Indianapolis, IN 46256, 317-572-3447, fax 317-572-4447, or e-mail permcoordinator@

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LIMIT OF LIABILITY/DISCLAIMER OF WARRANTY: THE PUBLISHER AND AUTHOR HAVE USED THEIR BEST

EFFORTS IN PREPARING THIS BOOK. THE PUBLISHER AND AUTHOR MAKE NO REPRESENTATIONS OR

WARRANTIES WITH RESPECT TO THE ACCURACY OR COMPLETENESS OF THE CONTENTS OF THIS BOOK

AND SPECIFICALLY DISCLAIM ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A

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SENTATIVES OR WRITTEN SALES MATERIALS. THE ACCURACY AND COMPLETENESS OF THE INFORMA-

TION PROVIDED HEREIN AND THE OPINIONS STATED HEREIN ARE NOT GUARANTEED OR WARRANTED

TO PRODUCE ANY PARTICULAR RESULTS, AND THE ADVICE AND STRATEGIES CONTAINED HEREIN MAY

NOT BE SUITABLE FOR EVERY INDIVIDUAL. NEITHER THE PUBLISHER NOR AUTHOR SHALL BE LIABLE

FOR ANY LOSS OF PROFIT OR ANY OTHER COMMERCIAL DAMAGES, INCLUDING BUT NOT LIMITED TO

SPECIAL, INCIDENTAL, CONSEQUENTIAL, OR OTHER DAMAGES.

Trademarks: Wiley, the Wiley Publishing logo, Cliffs, CliffsStudySolver, CliffsNotes, and CliffsAP are

trademarks or registered trademarks of John Wiley & Sons, Inc., and/or its affiliates and may not be

used without written permission. All other trademarks are the property of their respective owners.

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is a trademark of Wiley Publishing, Inc.

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Publisher’s Acknowledgments

Editorial

Project Editor: Kelly Dobbs Henthorne

Acquisitions Editor: Greg Tubach

Technical Editor: Anthony Bedenikovic

Editorial Assistant: Amanda Harbin

Composition

Project Coordinator: Kristie Rees

Indexer: Joan Griffitts

Proofreader: Laura L. Bowman

Wiley Publishing, Inc. Composition Services

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Table of Contents

Introduction xi

Terminology and Notation xi

Order of Operations xii

Graphing and the Coordinate Plane xiii

Simplifying Fractions xiii

Common Errors xiv

Pretest 1

Pretest Questions 1

Key to Pretest Questions 17

Chapter 1: The Basics 25

Rules for Exponents 25

Laws for Using Exponents 25

Adding and Subtracting Polynomials 27

Multiplying Polynomials 29

The FOIL Method 29

Special Products 31

Special Product #1 32

Special Product #2 32

Special Product #3 33

Special Product #4 34

Dividing Polynomials 36

Divisors with One Term 36

Long Division 36

Synthetic Division 39

Chapter Problems and Solutions 42

Problems 42

Answers and Solutions 43

Supplemental Chapter Problems 45

Problems 45

Answers 46

Chapter 2: Factoring and Solving Equations 49

Greatest Common Factors and Factoring Binomials 49

Greatest Common Factor 49

Factoring Binomials 52

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Factoring Trinomials 54

Factoring Other Polynomials 57

Quadratic-Like Expressions 57

Factoring by Grouping 58

Solving Quadratic Equations 60

Solving Quadratic Equations by Factoring 60

Solving Quadratic Equations with the Quadratic Formula 63

Solving Quadratic Equations Using Completing the Square 66

Solving Quadratic-Like Equations 71

Quadratic and Other Inequalities 74

Radical Equations with Quadratics 78

Chapter Problems and Solutions 81

Problems 81

Answers and Solutions 83

Supplemental Chapter Problems 85

Problems 85

Answers 86

Chapter 3: Function Operations and Transformations 89

Functions and Function Notation 89

Domain and Range 89

Function Notation 90

Function Operations 92

Addition, Subtraction, Multiplication, and Division 92

Composition of Functions 94

Difference Quotient 95

Inverse Functions 97

Showing That Two Functions Are Inverses of One Another 98

Solving for the Inverse of a Function 99

Function Transformations 100

Slides 101

Flips 101

Warps 102

Chapter Problems and Solutions 104

Problems 104

Answers and Solutions 106

Supplemental Chapter Problems 108

Answers 109

vi CliffsStudySolver Algebra II

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Chapter 4: Polynomials 111

Remainder Theorem 111

Rational Root Theorem and Descartes’ Rule of Sign 113

Rational Root Theorem 113

Descartes’ Rule of Sign 113

Upper and Lower Bounds 117

Using a Graphing Calculator to Graph Lines and Polynomials 119

Solving Equations and Inequalities Using Graphing 124

Chapter Problems and Solutions 129

Problems 129

Answers and Solutions 130

Supplemental Chapter Problems 135

Problems 135

Answers 136

Chapter 5: Exponential and Logarithmic Functions 141

Exponential Functions 141

Form y= ax142

Form y= a-x142

The Constant “e” 144

Compound Interest 146

Logarithmic Functions 149

Laws of Logarithms 151

Applications of Logarithms 153

Solving Exponential and Logarithmic Equations 156

Chapter Problems and Solutions 158

Problems 158

Answers and Solutions 160

Supplemental Chapter Problems 163

Problems 163

Answers 164

Chapter 6: Graphing 167

Graphing Polynomials 167

Graphing Rational Functions 172

Graphing Radical Functions 176

Graphing Absolute Value and Logarithmic Functions 181

Graphing Functions Using Transformations 188

Table of Contents vii

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Chapter Problems and Solutions 193

Problems 193

Answers and Solutions 194

Supplemental Chapter Problems 207

Problems 207

Answers 208

Chapter 7: Other Equations 217

Radical Equations and Conjugates 217

Rationalizing a Denominator 217

Radical Equations—Squaring More Than Once 218

Complex Numbers 220

Operations Involving Complex Numbers 222

Quadratic Formula and Complex Numbers 224

Rational Equations 226

Variation 228

Chapter Problems and Solutions 230

Problems 230

Answers and Solutions 232

Supplemental Chapter Problems 234

Problems 234

Answers 235

Chapter 8: Conic Sections 237

Circle 237

Area and Circumference 237

Standard Form 237

Changing to the Standard Form Using Completing the Square 238

Ellipse 240

Parabola 243

Hyperbola 245

Graphing Conics 247

Writing Equations of Circles 256

Chapter Problems and Solutions 259

Problems 259

Answers and Solutions 260

Supplemental Chapter Problems and Answers 265

Problems 265

Answers 266

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CliffsStudySolver™AlgebraIIByMaryJaneSterling01541358FM.qxd1/6/043:37PMPagei01541358FM.qxd1/6/043:37PMPageivCliffsStudySolver™AlgebraIIByMaryJaneSterling01541358FM.qxd1/6/043:37PMPageiPublishedby:WileyPublishing,Inc.111RiverStreetHoboken,NJ07030-5774www.wiley.comCopyright©2004WileyPublishing,Inc.New...

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