Algebra II Essentials For Dummies

195 Pages·2010·8.65 MB·English

by  Mary Jane Sterling

spine=.3840”
Mathematics/Algebra/General
Making Everything Easier!™
Jcuosntc tehpet sc ryiotiuc anleed Open the book and find: A l g e b r a I I
to score high in Algebra II
(cid:129) How to multiply and divide
A
exponents
Acolgnecbisrae IeI xEpsslaennatitaiolsn Fso or fD curmitimcaile cs osnticcekps ttso ttahueg phot iinnt a, w ith (cid:129) Ienqsutrauticotniosns for solving linear lge E s s e n t i a l s
typical Algebra II course. It’s perfect for cramming, for b
homework help, or as a reference for parents helping (cid:129) The quadratic formula r
students prepare for an exam. a
(cid:129) How to denote function notation
I
I
(cid:129) Play by the rules — get the lowdown on algebraic
(cid:129) Graphing techniques E
properties, exponential rules, and factoring
s
techniques
(cid:129) Introducing zero to find s
(cid:129) Be rational — follow easy-to-grasp instructions y-intercepts e
n
for working with rational and radical equations,
(cid:129) The steps to solving systems of t
from dealing with negative exponents to fiddling
equations i
with fractional exponents a
l
(cid:129) Know your functions — discover how to use (cid:129) Formulas you need to know s
exponential and logarithmic functions to solve
algebraic problems
(cid:129) Cozy up with polynomials — learn the steps to
confidently (and correctly) solve polynomial
equations Learn:
(cid:129) Exactly what you need to know
on exponential functions
Go to Dummies.com
®
for videos, step-by-step photos, (cid:129) The “must-know” laws of
how-to articles, or to shop! logarithms
(cid:129) Matrices, sequences, series, and
sets in quick, focused lessons
$9.99 US / $11.99 CN / £6.99 UK
Mary Jane Sterling is professor of
ISBN 978-0-470-61840-0
mathematics at Bradley University and
author of several books, including
Algebra II For Dummies and Algebra II
Workbook For Dummies.
Mary Jane Sterling
Sterling Professor of Mathematics
0022__661188440000--ffttoocc..iinndddd vvii 44//99//1100 1111::2288 AAMM
Algebra II
Essentials
FOR
DUMmIES
‰
by Mary Jane Sterling
0011__661188440000--ffffiirrss..iinndddd ii 44//99//1100 1111::2288 AAMM
Algebra II Essentials For Dummies®
Published by
Wiley Publishing, Inc.
111 River St.
Hoboken, NJ 07030-5774
www.wiley.com
Copyright © 2010 by Wiley Publishing, Inc., Indianapolis, Indiana
Published simultaneously in Canada
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 permission of the Publisher, or authorization through payment of the appro-
priate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923,
[phone], fax [phone]. Requests to the Publisher for permission should be addressed to
the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-
6011, fax [phone], or online at http://www.wiley.com/go/permissions.
Trademarks: Wiley, the Wiley Publishing logo, For Dummies, the Dummies Man logo, A Reference
for the Rest of Us!, The Dummies Way, Dummies Daily, The Fun and Easy Way, Dummies.com,
Making Everything Easier, and related trade dress are trademarks or registered trademarks of John
Wiley & Sons, Inc. and/or its affiliates in the United States and other countries, and may not be used
without written permission. All other trademarks are the property of their respective owners. Wiley
Publishing, Inc., is not associated with any product or vendor mentioned in this book.
LIMIT OF LIABILITY/DISCLAIMER OF WARRANTY: THE PUBLISHER AND THE AUTHOR MAKE
NO REPRESENTATIONS OR WARRANTIES WITH RESPECT TO THE ACCURACY OR COMPLETE-
NESS OF THE CONTENTS OF THIS WORK AND SPECIFICALLY DISCLAIM ALL WARRANTIES,
INCLUDING WITHOUT LIMITATION WARRANTIES OF FITNESS FOR A PARTICULAR PURPOSE.
NO WARRANTY MAY BE CREATED OR EXTENDED BY SALES OR PROMOTIONAL MATERIALS.
THE ADVICE AND STRATEGIES CONTAINED HEREIN MAY NOT BE SUITABLE FOR EVERY SITU-
ATION. THIS WORK IS SOLD WITH THE UNDERSTANDING THAT THE PUBLISHER IS NOT
ENGAGED IN RENDERING LEGAL, ACCOUNTING, OR OTHER PROFESSIONAL SERVICES. IF PRO-
FESSIONAL ASSISTANCE IS REQUIRED, THE SERVICES OF A COMPETENT PROFESSIONAL
PERSON SHOULD BE SOUGHT. NEITHER THE PUBLISHER NOR THE AUTHOR SHALL BE LIABLE
FOR DAMAGES ARISING HEREFROM. THE FACT THAT AN ORGANIZATION OR WEBSITE IS
REFERRED TO IN THIS WORK AS A CITATION AND/OR A POTENTIAL SOURCE OF FURTHER
INFORMATION DOES NOT MEAN THAT THE AUTHOR OR THE PUBLISHER ENDORSES THE
INFORMATION THE ORGANIZATION OR WEBSITE MAY PROVIDE OR RECOMMENDATIONS IT
MAY MAKE. FURTHER, READERS SHOULD BE AWARE THAT INTERNET WEBSITES LISTED IN
THIS WORK MAY HAVE CHANGED OR DISAPPEARED BETWEEN WHEN THIS WORK WAS WRIT-
TEN AND WHEN IT IS READ.
For general information on our other products and services, please contact our Customer Care
Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax [phone].
For technical support, please visit www.wiley.com/techsupport.
Wiley also publishes its books in a variety of electronic formats. Some content that appears in print
may not be available in electronic books.
Library of Congress Control Number: 2010925242
ISBN: 978-0-470-61840-0
Manufactured in the United States of America
10 9 8 7 6 5 4 3 2 1
0011__661188440000--ffffiirrss..iinndddd iiii 44//99//1100 1111::2288 AAMM
About the Author
Mary Jane Sterling has been an educator since graduating
from college. Teaching at the junior high, high school, and
college levels, she has had the full span of experiences and
opportunities to determine how best to explain how mathe-
matics works. She has been teaching at Bradley University in
Peoria, Illinois, for the past 30 years. She is also the author of
Algebra II For Dummies, Trigonometry For Dummies, Math Word
Problems For Dummies, Business Math For Dummies, and Linear
Algebra For Dummies.
0011__661188440000--ffffiirrss..iinndddd iiiiii 44//99//1100 1111::2288 AAMM
Publisher’s Acknowledgments
We’re proud of this book; please send us your comments at http://dummies.
custhelp.com. For other comments, please contact our Customer Care Department
within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax [phone].
Some of the people who helped bring this book to market include the following:
Acquisitions, Editorial, and Composition Services
Media Development
Project Coordinator:
Project Editor: Elizabeth Kuball Sheree Montgomery
Senior Acquisitions Editor: Layout and Graphics: Carl Byers,
Lindsay Sandman Lefevere Carrie A. Cesavice, Joyce Haughey,
Mark Pinto
Copy Editor: Elizabeth Kuball
Proofreaders: Melissa Cossell,
Assistant Editor: Erin Calligan Mooney
Tricia Liebig
Editorial Program Coordinator:
Indexer: Potomac Indexing, LLC
Joe Niesen
Technical Editors: Tony Bedenikovic,
Stefanie Long
Senior Editorial Manager:
Jennifer Ehrlich
Editorial Supervisor and Reprint Editor:
Carmen Krikorian
Senior Editorial Assistant: David Lutton
Editorial Assistants: Rachelle Amick,
Jennette ElNaggar
Cover Photos: ©iStock
Cartoons: Rich Tennant
(www.the5thwave.com)
Publishing and Editorial for Consumer Dummies
Diane Graves Steele, Vice President and Publisher, Consumer Dummies
Kristin Ferguson-Wagstaffe, Product Development Director, Consumer Dummies
Ensley Eikenburg, Associate Publisher, Travel
Kelly Regan, Editorial Director, Travel
Publishing for Technology Dummies
Andy Cummings, Vice President and Publisher, Dummies Technology/General User
Composition Services
Debbie Stailey, Director of Composition Services
0011__661188440000--ffffiirrss..iinndddd iivv 44//99//1100 1111::2288 AAMM
Contents at a Glance
Introduction ...............................................................................................1
Chapter 1: Making Advances in Algebra .................................................5
Chapter 2: Lining Up Linear Equations .................................................15
Chapter 3: Making Quick Work of Quadratic Equations.....................23
Chapter 4: Rolling Along with Rational and Radical Equations .........35
Chapter 5: Forging Function Facts ........................................................47
Chapter 6: Graphing Linear and Quadratic Functions ........................61
Chapter 7: Pondering Polynomials ........................................................75
Chapter 8: Being Respectful of Rational Functions .............................91
Chapter 9: Examining Exponential and Logarithmic Functions ......107
Chapter 10: Getting Creative with Conics ..........................................121
Chapter 11: Solving Systems of Equations .........................................135
Chapter 12: Taking the Complexity Out of Complex Numbers .......157
Chapter 13: Ten (Or So) Special Formulas .........................................165
Index........................................................................................................171

0022__661188440000--ffttoocc..iinndddd vv 44//99//1100 1111::2288 AAMM
0022__661188440000--ffttoocc..iinndddd vvii 44//99//1100 1111::2288 AAMM
Table of Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
About This Book ........................................................................1
Conventions Used in This Book ...............................................2
Foolish Assumptions .................................................................2
Icons Used in This Book ............................................................2
Where to Go from Here .............................................................3
Chapter 1: Making Advances in Algebra . . . . . . . . . . . . .5
Bringing Out the Best in Algebraic Properties .......................5
Making short work of the basic properties ..................6
Organizing your operations............................................8
Enumerating Exponential Rules ...............................................8
Multiplying and dividing exponents ..............................9
Rooting out exponents ....................................................9
Powering up exponents ................................................10
Working with negative exponents ...............................10
Assigning Factoring Techniques ............................................11
Making two terms factor ...............................................11
Factoring three terms....................................................12
Factoring four or more terms by grouping.................14
Chapter 2: Lining Up Linear Equations . . . . . . . . . . . . . .15
Getting the First Degree: Linear Equations ...........................15
Solving basic linear equations .....................................16
Eliminating fractions .....................................................16
Lining Up Linear Inequalities ..................................................17
Solving basic inequalities .............................................18
Introducing interval notation .......................................19
Absolute Value: Keeping Everything in Line ........................20
Solving absolute value equations ................................20
Seeing through absolute value inequality ..................21
Chapter 3: Making Quick Work
of Quadratic Equations . . . . . . . . . . . . . . . . . . . . . . . . .23
Using the Square Root Rule When Possible .........................24
Solving Quadratic Equations by Factoring ...........................25
Factoring quadratic binomials .....................................25
Factoring quadratic trinomials ....................................26
0022__661188440000--ffttoocc..iinndddd vviiii 44//99//1100 1111::2288 AAMM
viii
Algebra II Essentials For Dummies
The Quadratic Formula to the Rescue ..................................27
Realizing rational solutions ..........................................27
Investigating irrational solutions .................................28
Promoting Quadratic-like Equations .....................................28
Solving Quadratic Inequalities ...............................................29
Keeping it strictly quadratic.........................................30
Signing up for fractions .................................................32
Increasing the number of factors ................................33
Chapter 4: Rolling Along with Rational
and Radical Equations . . . . . . . . . . . . . . . . . . . . . . . . . .35
Rounding Up Rational Equations
and Eliminating Fractions ...................................................35
Making your least common denominator
work for you ...............................................................36
Proposing proportions for solving
rational equations ......................................................38
Reasoning with Radicals .........................................................39
Squaring both sides of the equation ...........................40
Taking on two radicals ..................................................41
Dealing with Negative Exponents ..........................................42
Factoring out a negative exponent as a greatest
common factor ...........................................................43
Solving quadratic-like trinomials .................................44
Fiddling with Fractional Exponents .......................................45
Solving equations by factoring
fractional exponents ..................................................45
Promoting techniques for working
with fractional exponents .........................................45
Chapter 5: Forging Function Facts . . . . . . . . . . . . . . . . . .47
Describing Function Characteristics .....................................47
Denoting function notation ..........................................48
Using function notation to evaluate functions ...........48
Determining Domain and Range.............................................49
Delving into domain ......................................................49
Wrangling with range ....................................................50
Counting on Even and Odd Functions ...................................51
Determining whether even or odd ..............................52
Using even and odd functions in graphs ....................53
Taking on Functions One-to-One............................................53
Defining which functions are one-to-one ....................54
Testing for one-to-one functions ..................................54
0022__661188440000--ffttoocc..iinndddd vviiiiii 44//99//1100 1111::2288 AAMM