Holt Algebra 2

1112 Pages·2003·40.34 MB·English

A Harcourt Education Company
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i
Copyright © 2004 by Holt, Rinehart and Winston
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Acknowledgments appear on pages 1093-1094, which are extensions of the copyright page.
Printed in the United States of America
ISBN: 0-03-070044-2
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FM pi-pv 5/21/03 7:31 AM Page iii
A U T H O R S
James E.Schultz,Senior Series Author
Dr.Schultz has over 30 years ofexperience teaching at the high school and college
levels and is the Robert L.Morton Professor ofMathematics Education at Ohio
University.He helped to establish standards for mathematics instruction as a co-
author ofthe NCTM Curriculum and Evaluation Standards for School Mathematics
andA Core Curriculum: Making Mathematics Count for Everyone.
Wade Ellis,Jr.,Senior Author
Professor Ellis has co-authored numerous books and articles on how to integrate
technology realistically and meaningfully into the mathematics curriculum.He was a
key contributor to the landmark study Everybody Counts: A Report to the Nation on
the Future ofMathematics Education.
Kathleen A.Hollowell
Dr.Hollowell is an experienced high school mathematics and computer science
teacher who currently serves as Director ofthe Mathematics & Science Education
Resource Center,University ofDelaware.Dr.Hollowell is particularly well versed in
the special challenge ofmotivating students and making the classroom a more
dynamic place to learn.
Paul A.Kennedy
A professor in the Department ofMathematics at Colorado State University,Dr.
Kennedy is a leader in mathematics education reform.His research focuses on
developing algebraic thinking by using multiple representations and technology.He
has been the author ofnumerous publications and he is often invited to speak and
conduct workshops on the teaching ofsecondary mathematics.
iii
C O N T R I B U T I N G A U T H O R
Martin Engelbrecht
A mathematics teacher at Culver Academies,Culver,Indiana,Mr.Engelbrecht also
teaches statistics at Purdue University,North Central.An innovative teacher and
writer,he integrates applied mathematics with technology to make mathematics
accessible to all students.
T E C H N O L O G Y W R I T E R A N D C O N S U L T A N T
Betty Mayberry
Ms.Mayberry is the mathematics department chair at Gallatin High School,Gallatin,
Tennessee.She has received the Presidential Award for Excellence in Teaching
Mathematics and the Tandy Technology Scholar award.She is a Teachers Teaching
with Technology instructor and a popular speaker for the effective use oftechnology
in mathematics instruction.
iv
R E V I E W E R S
Reba W.Allen Cheryl Mockel
Gallatin High School Mt.Spokane High School
Gallatin,TN Mead,WA
Judy B.Basara Steve Murray
St.Hubert High School Cerritos High School
Philadelphia,PA Huntington Beach,CA
Audrey M.Beres Stacey Pearson
Bassick High School North Gaston High School
Bridgeport,CT Dallas,NC
Mark Budahl James R.Ringstrom
Mitchell High School La Costa Canyon High School
Mitchell,SD Carlsbad,CA
Michael Chronister Douglas E.Roberts
J.K.Mullen High School Franklin Heights High School
Denver,CO Columbus,OH
Suellyn Chronister Alice B.Robertson
Littleton High School Central High School
Littleton,CO Carrolton,GA
Craig Duncan James F.Rybolt
The Chinquapin School Mt.Diablo USA
Highlands,TX Antioch,CA
Robert S.Formentelli Jeffrey C.Schmook
Uniontown Area High School Yough Senior High School
Uniontown,PA Herminie,PA
Richard Frankenberger Harry Sirockman
Hazelwood School District Central Catholic High School
Florissant,MO Pittsburgh,PA
Mary Hutchinson Richard Soendlin
South Mecklenburg High School Arsenal Technical High School
Charlotte,NC Indianapolis,IN
James A.Kohr Charleen Strain
Eldorado High School Roswell High School
Albuquerque,NM Roswell,NM
David Landreth Harry D.Stratigos
Carlsbad Senior High School Pennsylvania Department ofEducation
Carlsbad,NM Harrisburg,PA
Pam Mason JeffVollmer
Mathematics Advisor Myers Park High School
Austin,TX Charlotte,NC
Gilbert Melendez
Gasden High School
Las Cruces,NM
v
Table of Contents
DATA AND LINEAR REPRESENTATIONS 2
1.1 Tables and Graphs of Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Slopes and Intercepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 Linear Equations in Two Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.4 Direct Variation and Proportion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.5 Scatter Plots and Least-Squares Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
1.6 Introduction to Solving Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Eyewitness Math:A Man and a Method . . . . . . . . . . . . . . . . . . . . . . . . . 52
1.7 Introduction to Solving Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
1.8 Solving Absolute-Value Equations and Inequalities . . . . . . . . . . . . . . . . . 61
Chapter Project:Correlation Exploration. . . . . . . . . . . . . . . . . . . . . . . . . 70
Chapter Review and Assessment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Cumulative Assessment:College Entrance Exam Practice . . . . . . . . . . 78
Keystroke Guide for Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4,13,23,31,37,47,56,63
Extra Practice for Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 942
MATH CONNECTIONS
Coordinate Geometry23, 27, 34 Statistics38, 39, 60, 74
Geometry31, 35, 47, 49, 75, 76, 79
A P P L I C AT I O N S
Science Business and Life Skills
Agriculture 19, 44 Economics Academics 28, 56, 58
Anatomy 42, 79 Business 10, 60, 75 Banking 50
Health 37, 43, 59, 68 Communications 12 Freight Charges 74
Medicine 48 Construction 19, 77 Fund-raising 59
Meteorology 10, 19, 69 Consumer Economics 50, Income 4, 5, 8, 9, 28, 33,
Physics 19, 32, 33, 35, 36 75 50, 51
Temperature 46 Economics 10 Personal Finance 76
Manufacturing 61, 66
Social Studies Sports and Leisure
Marketing 42
Demographics 10, 40 Entertainment 68
Real Estate 69
Government 43, 60 Recreation 29, 30, 50,
Sales Tax 7
Psychology 72 51, 67, 69
Taxes 18, 40, 50, 54
Sports 39, 41, 69, 77
Language Arts
Travel 21, 22, 25, 27, 60
Communicate 7, 17,
25, 33, 40, 48, 57, 67
Etymology 42, 69
vi TABLE OF CONTENTS
NUMBERS AND FUNCTIONS 84
2.1 Operations With Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
2.2 Properties of Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
2.3 Introduction to Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
2.4 Operations With Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
2.5 Inverses of Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
2.6 Special Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
2.7 A Preview of Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Chapter Project:Space Trash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Chapter Review and Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Cumulative Assessment:College Entrance Exam Practice . . . . . . . . . 148
Keystroke Guide for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89,95,104,111,119,124,133
Extra Practice for Chapter 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 946
MATH CONNECTIONS
Geometry99, 102, 104, 109 Transformations126, 127, 130, 132
Statistics91, 149
A P P L I C AT I O N S
Science Language Arts Life Skills
Chemistry 100, 121, 147 Communicate 90, 98, 107, Consumer Economics 106,
Engineering 100 114, 121, 128, 139 109, 114, 115, 117, 123,
Health 133 Etymology 90 126, 129, 131, 132, 146,
Medicine 97, 98 149
Business and
Meteorology 86 Income 107, 108, 124, 131
Physics 94, 98, 100, 141 Economics Transportation 107, 111
Space Science 93, 101, Business 90, 92, 116, 123
110, 117, 132 Manufacturing 116, 128, Sports and Leisure
Temperature 116, 118 129, 130 Entertainment 102
Real Estate 123 Puzzles 123
Social Studies Taxes 88 Sports 146
Current Events 92
Other
Demographics 92, 116
Genealogy 101
TABLE OF CONTENTS vii
SYSTEMS OF LINEAR EQUATIONS & INEQUALITIES 154
3.1 Solving Systems by Graphing or Substitution . . . . . . . . . . . . . . . . . . . . 156
3.2 Solving Systems by Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
3.3 Linear Inequalities in Two Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
3.4 Systems of Linear Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
3.5 Linear Programming. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
3.6 Parametric Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
Chapter Project:Maximum Profit/Minimum Cost . . . . . . . . . . . . . . . . . 202
Chapter Review and Assessment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Cumulative Assessment:College Entrance Exam Practice . . . . . . . . . 208
Keystroke Guide for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
Activities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156,166,175,182,188,195
Extra Practice for Chapter 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 949
MATH CONNECTIONS
Coordinate Geometry169 Maximum/Minimum188, 189, 190,
Geometry162, 177, 184, 192 191, 192
Transformations197, 200, 201
A P P L I C AT I O N S
Science Business and Life Skills
Agriculture 187, 188, 191, Economics Consumer Economics 163,
193 Broadcasting 206 178
Aviation 195, 201 Business 164, 165, 168, Fund-raising 177
Chemistry 156, 158, 163 170, 171, 185, 186, 193, Income 162, 170, 185, 209
Engineering 209 194 Transportation 193
Health 182, 193, 201 Economics 207
Sports and Leisure
Nutrition 170 Fuel Economy 172, 174,
Drama 179
176
Language Arts Entertainment 185
Investments 170
Communicate 160, 168, Recreation 177
Landscaping 171
176, 182, 191, 199 Sports 163, 170, 177, 198,
Manufacturing 184, 192,
Synonyms 186 199, 200, 206
206, 209
Small Business 161, 178, Other
194
Criminology 184
viii TABLE OF CONTENTS
MATRICES 214
4.1 Using Matrices to Represent Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
4.2 Matrix Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
4.3 The Inverse of a Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
Eyewitness Math:How Secret Is Secret? . . . . . . . . . . . . . . . . . . . . . . . . . 242
4.4 Solving Systems With Matrix Equations . . . . . . . . . . . . . . . . . . . . . . . . . 244
4.5 Using Matrix Row Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Chapter Project:Spell Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
Chapter Review and Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
Cumulative Assessment:College Entrance Exam Practice . . . . . . . . . 266
Keystroke Guide for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227,238,246,255
Extra Practice for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 952
MATH CONNECTIONS
Coordinate Geometry219, 221, 227, Probability258
230, 241 Transformations220, 221, 222, 230,
Geometry249, 255 265
A P P L I C AT I O N S
Science Business and Life Skills
Anatomy 267 Economics Academics 223
Chemistry 250 Business 259 Consumer Economics 223
Cryptography 234, 237, Inventory 216, 218, 221, Fund-raising 264
239, 241 223, 232
Sports and Leisure
Networks 228, 229, 232, Investments 244, 245, 248,
233 250 Entertainment 249
Nutrition 227, 229, 230, Manufacturing 256, 258 Sports 225, 231, 232, 267
231 Rentals 233 Travel 259
Social Studies Small Business 251, 253, Other
267
Geography 222 Jewelry 263
Language Arts
Communicate 220, 229,
239, 248, 256
TABLE OF CONTENTS ix
QUADRATIC FUNCTIONS 272
5.1 Introduction to Quadratic Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . 274
5.2 Introduction to Solving Quadratic Equations . . . . . . . . . . . . . . . . . . . . 281
5.3 Factoring Quadratic Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
5.4 Completing the Square . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
5.5 The Quadratic Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
5.6 Quadratic Equations and Complex Numbers . . . . . . . . . . . . . . . . . . . . 314
5.7 Curve Fitting With Quadratic Models . . . . . . . . . . . . . . . . . . . . . . . . . . 322
5.8 Solving Quadratic Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
Chapter Project:Out ofThis World . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
Chapter Review and Assessment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340
Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
Cumulative Assessment:College Entrance Exam Practice . . . . . . . . . 346
Keystroke Guide for Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
Activities . . . . . . . . . . . . . . . . . . . . . . 275,283,291,299,309,317,326,330
Extra Practice for Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 955
Ancient clay tablet MATH CONNECTIONS
believed to contain
Coordinate Geometry318, 321 Patterns in Data328
Pythagorean triples Geometry284, 285, 286, 287, 288, 296, Statistics323, 325
297, 305, 345 Transformations279, 289, 302, 304,
Maximum/Minimum276, 277, 278, 306, 321, 345
312, 335
A P P L I C AT I O N S
Science Business and Highway Safety 322, 325,
Architecture 290, 295 Economics 327
Aviation 286, 344 Advertising 298 Recycling 321
Chemistry 347 Business 312, 321, 328,
Sports and Leisure
Engineering 285, 288, 299, 336, 347
Art 312
303, 314, 345 Construction 279, 286,
Recreation 288, 344
Navigation 288 289, 307, 309, 311
Sports 280, 288, 289, 297,
Physics 274, 288, 305, 328, Manufacturing 312
298, 304, 306, 313, 329,
329, 336, 337, 345, 347 Small Business 330, 332,
336, 337
Rescue 281, 283 336, 337
Telecommunications 288
Language Arts
Communicate 277, 286, Life Skills
295, 303, 310, 319, 326, Fund-raising 279, 305
334