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5703SwokowskiFrontEndpapers 1/12/07 3:10 PM Page 2 ALGEBRA QUADRATIC FORMULA SPECIAL PRODUCT FORMULAS SPECIAL FACTORING FORMULAS If a(cid:1)0,the roots of (cid:1)x(cid:4)y(cid:2)(cid:1)x(cid:6)y(cid:2)(cid:1)x2(cid:6)y2 x2(cid:6)y2(cid:1)(cid:1)x(cid:4)y(cid:2)(cid:1)x(cid:6)y(cid:2) ax2(cid:4)bx(cid:4)c(cid:1)0are (cid:1)x(cid:4)y(cid:2)2(cid:1)x2(cid:4)2xy (cid:4)y2 x2(cid:4)2xy (cid:4)y2(cid:1)(cid:1)x(cid:4)y(cid:2)2 (cid:6)b(cid:7) 2b2(cid:6) 4ac x(cid:1) (cid:1)x(cid:6)y(cid:2)2(cid:1)x2(cid:6)2xy (cid:4)y2 x2(cid:6)2xy (cid:4)y2(cid:1)(cid:1)x(cid:6)y(cid:2)2 2a (cid:1)x(cid:4)y(cid:2)3(cid:1)x3(cid:4)3x2y(cid:4)3xy2(cid:4)y3 x3(cid:6)y3(cid:1)(cid:1)x(cid:6)y(cid:2)(cid:1)x2(cid:4)xy (cid:4) y2(cid:2) (cid:1)x(cid:6)y(cid:2)3(cid:1)x3(cid:6)3x2y(cid:4)3xy2(cid:6)y3 x3(cid:4)y3(cid:1)(cid:1)x(cid:4)y(cid:2)(cid:1)x2(cid:6)xy (cid:4) y2(cid:2) EXPONENTS AND RADICALS BINOMIAL THEOREM INEQUALITIES (cid:6) (cid:7) (cid:6) (cid:7) aman (cid:1)am(cid:4)n a1/n(cid:1) 2n a n n If a(cid:3)band b(cid:3)c,then a(cid:3) c (cid:1)x(cid:4)y(cid:2)n(cid:1)xn(cid:4) xn(cid:6)1y(cid:4) xn(cid:6)2y2(cid:4) (cid:1)am(cid:2)n(cid:1)amn am/n (cid:1) 2n am (cid:6)1 (cid:7) 2 If a(cid:3)b,then a(cid:4)c(cid:3)b(cid:4)c (cid:6)(cid:1)ab(cid:2)(cid:7)n(cid:1)anbn am/n (cid:1)(cid:1)2n a(cid:2)m (cid:2)(cid:2)(cid:2)(cid:4) n xn(cid:6)kyk(cid:4) (cid:2)(cid:2)(cid:2)(cid:4)yn, If a(cid:3)band c(cid:3)0,then ac (cid:3) bc (cid:6) (cid:7) k a n an If a(cid:3)band c(cid:5)0,then ac (cid:5) bc (cid:1) 2n ab(cid:1) 2n a 2n b n n! b bn (cid:5) where (cid:1) k k!(cid:1)n(cid:6)k(cid:2)! am a 2n a (cid:1)am(cid:6)n n (cid:1) an b 2n b 1 a(cid:6)n(cid:1) (cid:4)m2n a(cid:1) 2mna an ABSOLUTE VALUE (cid:1)d(cid:3) 0(cid:2) SEQUENCES EXPONENTIALS AND LOGARITHMS (cid:3)x(cid:3)(cid:5)dif and only if nth term of an arithmetic sequence with first y(cid:1)log x means ay(cid:1)x a (cid:6)d(cid:5)x(cid:5)d term a1and common difference d log xy (cid:1)log x(cid:4)log y a a a (cid:3)x(cid:3) (cid:3)dif and only if either an(cid:1)a1(cid:4)(cid:1)n(cid:6)1(cid:2)d x log (cid:1)log x(cid:6)log y x(cid:3)d or x(cid:5)(cid:6)d Sum S of the first nterms of an arithmetic a y a a n sequence log xr(cid:1)rlog x MEANS S (cid:1) n (cid:1)a (cid:4)a(cid:2) a a n 2 1 n alogax(cid:1)x Arithmetic mean Aof nnumbers n log ax(cid:1)x or S (cid:1) (cid:8)2a (cid:4)(cid:1)n(cid:6)1(cid:2)d(cid:9) a a (cid:4)a (cid:4)(cid:2)(cid:2)(cid:2)(cid:4)a n 2 1 A(cid:1) 1 2 n log 1(cid:1)0 a n nth term of a geometric sequence with first log a(cid:1)1 term a and common ratio r a Geometric mean Gof nnumbers 1 logx(cid:1)log x a (cid:1)arn(cid:6)1 10 G(cid:1)(cid:1)a1a2(cid:2)(cid:2)(cid:2)an(cid:2)1/n,ak(cid:3)0 n 1 lnx(cid:1)log x Sum S of the first nterms of a geometric e n sequence log u log u(cid:1) a a(cid:1)1(cid:6)rn(cid:2) b logab S (cid:1) 1 n 1(cid:6)r Copyright 2008 Thomson Learning, Inc. 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May not be copied, scanned, or duplicated, in whole or in part. 5703SwokowskiFrontEndpapers 1/12/07 3:10 PM Page 3 FORMULAS FROM GEOMETRY area A perimeterP circumference C volume V curved surface area S altitude h radius r RIGHT TRIANGLE TRIANGLE EQUILATERAL TRIANGLE c a c a s s h h b b s 23 23 Pythagorean Theorem:c2(cid:1) a2(cid:4) b2 A (cid:1) 1bh P (cid:1) a (cid:4) b (cid:4) c h (cid:1) s A (cid:1) s2 2 2 4 RECTANGLE PARALLELOGRAM TRAPEZOID a w h h l b b A (cid:1) lw P (cid:1) 2l(cid:4) 2w A (cid:1) bh A (cid:1) 1(cid:1)a (cid:4) b(cid:2)h 2 CIRCLE CIRCULAR SECTOR CIRCULAR RING r u s r r R A (cid:1) (cid:8)r2 C (cid:1) 2(cid:8)r A (cid:1) 1r2(cid:9) s (cid:1) r(cid:9) A (cid:1) (cid:8)(cid:1)R2(cid:6) r2(cid:2) 2 RECTANGULAR BOX SPHERE RIGHT CIRCULAR CYLINDER h h r w l r V (cid:1) lwh S (cid:1) 2(cid:1)hl(cid:4) lw (cid:4) hw(cid:2) V (cid:1) 4(cid:8)r3 S (cid:1) 4(cid:8)r2 V (cid:1) (cid:8)r2h S (cid:1) 2(cid:8)rh 3 RIGHT CIRCULAR CONE FRUSTUM OF A CONE PRISM r h h h r R V (cid:1) 1(cid:8)r2h S (cid:1) (cid:8)r2r2(cid:4) h2 V (cid:1) 1(cid:8)h(cid:1)r2(cid:4) rR (cid:4) R2(cid:2) V (cid:1) Bhwith Bthe area of the base 3 3 Copyright 2008 Thomson Learning, Inc. 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May not be copied, scanned, or duplicated, in whole or in part. 5703SwokowskiFrontEndpapers 1/12/07 3:10 PM Page 4 ANALYTIC GEOMETRY DISTANCE FORMULA EQUATION OF A CIRCLE d(cid:1)P,P(cid:2)(cid:1) 2(cid:1)x (cid:6)x(cid:2)2(cid:4)(cid:1)y (cid:6)y(cid:2)2 (cid:1)x(cid:6)h(cid:2)2(cid:4)(cid:1)y(cid:6)k(cid:2)2(cid:1)r2 1 2 2 1 2 1 y y r (h, k) P1(x1, y1) P2(x2, y2) x x SLOPE mOF A LINE GRAPH OF A QUADRATIC FUNCTION y (cid:6)y y(cid:1)ax2,a(cid:3)0 y(cid:1)ax2(cid:4)bx(cid:4)c,a(cid:3)0 y m(cid:1) 2 1 l x2(cid:6)x1 y y (x, y ) (x , y ) c 1 1 2 2 x x (cid:6) b x 2a POINT-SLOPE FORM OF A LINE CONSTANTS y y(cid:6)y (cid:1)m(cid:1)x(cid:6)x(cid:2) (cid:8)(cid:10)3.14159 1 1 l e(cid:10)2.71828 (x, y ) 1 1 CONVERSIONS x 1centimeter(cid:10)0.3937inch SLOPE-INTERCEPT FORM OF A LINE 1meter (cid:10)3.2808feet 1kilometer (cid:10)0.6214mile y y(cid:1)mx(cid:4)b 1gram (cid:10)0.0353ounce l (0, b) 1kilogram(cid:10)2.2046pounds 1liter (cid:10)0.2642gallon x 1milliliter (cid:10)0.0381fluid ounce INTERCEPT FORM OF A LINE 1joule(cid:10)0.7376foot-pound 1newton (cid:10)0.2248pound x y l y a (cid:4) b (cid:1)1 (cid:1)a(cid:1)0,b(cid:1)0(cid:2) 1lumen(cid:10)0.0015watt (0, b) 1acre(cid:1)43,560square feet (a, 0) x Copyright 2008 Thomson Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Swokowski AlgTrig insert 1/25/07 1:50 PM Page 1 www.webassign.net/brookscole This proven homework system Algorithmic problems for unlimited practice saves you time and gives your Choose from approximately 1,500 problems drawn directly from the text, including free- students effective tutorial support. response, multiple-choice, and multi-step problem types. Enhanced WebAssign generates Proven and reliable, Enhanced WebAssign allows you to easily assign, collect, grade, algorithmic versions of these problems, creating and record homework assignments via the web. This complete learning system for virtually unlimited practice opportunities for mathematics students includes 1,500 text-specific practice exercises as well as tutorials, students. video examples, and links to PDFs of sections of the text. 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Cole 0-495-01269-6 Calculus Texts by James Stewart College Algebra, Ninth Edition Calculus, Sixth Edition R. David Gustafson and Peter D. Frisk 0-495-01160-6 0-495-01266-1 Calculus: Early Transcendentals, Sixth Edition 0-495-01166-5 Precalculus: Mathematics for Calculus, Fifth Edition Essential Calculus James Stewart, Lothar Redlin, and Saleem Watson 0-495-01442-7 0-534-49277-0 Essential Calculus: Early Transcendentals 0-495-01428-1 Open here to learn more about how Enhanced WebAssign can work for you! Copyright 2008 Thomson Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. 5703_Swokowski_ATWAG_FM 1/12/07 3:13 PM Page i TWELFTH EDITION ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY EARL W. SWOKOWSKI JEFFERY A. COLE Anoka-Ramsey Community College Australia • Brazil • Canada • Mexico • Singapore • Spain United Kingdom • United States Copyright 2008 Thomson Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. 5703_Swokowski_ATWAG_FM 1/26/07 4:06 PM Page ii Algebra and Trigonometry with Analytic Geometry, 12e Earl W. Swokowski and Jeffery A.Cole Acquisitions Editor:Gary Whalen Creative Director:Vernon Boes Development Editors:Kari Hopperstead/Leslie Lahr Print Buyer:Judy Inouye Assistant Editor:Dianna Muhammad Production Service:Lifland et al.,Bookmakers Editorial Assistant:Lynh Pham Text Designers:Andrew Ogus/Rokusek Technology Project Manager:Donna Kelley Cover Designer:Bill Stanton Marketing Manager:Joe Rogove Cover Image:Scott Tysick/Masterfile Marketing Assistant:Jennifer Liang Compositor:Better Graphics,Inc. Marketing Communications Manager:Darlene Amidon-Brent Cover and Interior Printer:R R Donnelley—Willard Content Project Manager:Janet Hill COPYRIGHT ©2008 Thomson Brooks/Cole,a part of The Thomson Thomson Higher Education Corporation. 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Windows is a registered trademark of the Microsoft Corporation used herein under license. Macintosh and Power Macintosh are registered trademarks of Apple Computer,Inc.Used herein under license. ©2008 Thomson Learning,Inc. AllRights Reserved. Thomson Learning WebTutorTMis a trademark of Thomson Learning,Inc. Library of Congress Control Number:2007920848 Student Edition: ISBN-13:978-0-495-10826-9 ISBN-10:0-495-10826-X Copyright 2008 Thomson Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. 5703_Swokowski_ATWAG_FM 1/10/07 4:55 PM Page iii To the memory of Earl W. Swokowski Copyright 2008 Thomson Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. 5703_Swokowski_ATWAG_FM 1/10/07 4:55 PM Page iv CONTENTS List of Graphing Calculator Topics viii Preface x CHAPTER 1 Fundamental Concepts of Algebra 1 1.1 Real Numbers 2 1.2 Exponents and Radicals 19 1.3 Algebraic Expressions 31 1.4 Fractional Expressions 45 Chapter 1 Review Exercises 56 Chapter 1 Discussion Exercises 58 CHAPTER 2 Equations and Inequalities 59 2.1 Equations 60 2.2 Applied Problems 69 2.3 Quadratic Equations 80 2.4 Complex Numbers 95 2.5 Other Types of Equations 103 2.6 Inequalities 112 2.7 More on Inequalities 121 Chapter 2 Review Exercises 129 Chapter 2 Discussion Exercises 132 CHAPTER 3 Functions and Graphs 133 3.1 Rectangular Coordinate Systems 134 3.2 Graphs of Equations 143 3.3 Lines 159 3.4 Definition of Function 178 3.5 Graphs of Functions 196 3.6 Quadratic Functions 213 iv Copyright 2008 Thomson Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.