## Overview

Using authentic data to make math meaningful to students, **Jay Lehmann’s algebra series** uses a curve-fitting approach to model compelling, real-world situations, while answering the perennial question “But what is this good for?” Beginning with interesting data sets, students are asked to find models and derive equations to fit a scenario, helping them to understand functions graphically, numerically, and symbolically. Updated exercises, labs, and graphs deepen students’ understanding of core concepts and keeps them motivated to learn.

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**0321868277 / 9780321868275 Elementary Algebra: Graphs and Authentic Applications **

## Table of contents

Preface

To the student

Acknowledgments

Index of applications

**1. Introduction to Modeling**

1.1 Variables and Constants

1.2 Scattergrams

1.3 Exact Linear Relationships

1.4 Approximate Linear Relationships

Taking it to the Lab: Climate Change Lab * Volume Lab * Linear

Graphing Lab: Topic of Your Choice

CHAPTER SUMMARY

Key Points of Chapter 1

Chapter 1 Review Exercises

Chapter 1 Test

**2. Operations and Expressions**

2.1 Expressions

2.2 Operations with Fractions

2.3 Adding Real Numbers

2.4 Change in a Quantity and Subtracting Real Numbers

2.5 Ratios, Percents, and Multiplying and Dividing Real Numbers

2.6 Exponents and Order of Operations

Taking it to the Lab: Climate Change Lab * Stocks Lab

CHAPTER SUMMARY

Key Points of Chapter 2

Chapter 2 Review Exercises

Chapter 2 Test

Cumulative Review of Chapters 1 and 2

**3. Using Slope to Graph Linear Equations**

3.1 Graphing Equations of the Form *y = mx + b*

3.2 Graphing Linear Models; Unit Analysis

3.3 Slope of a Line

3.4 Using Slope to Graph Linear Equations

3.5 Rate of Change

Taking it to the Lab: Climate Change Lab * Workout

Lab * Balloon Lab

CHAPTER SUMMARY

Key Points of Chapter 3

Chapter 3 Review Exercises

Chapter 3 Test

**4. Simplifying Expressions and Solving Equations**

4.1 Commutative, Associative, and Distributive Laws

4.2 Simplifying Expressions

4.3 Solving Linear Equations in One Variable

4.4 Solving More Linear Equations in One Variable

4.5 Comparing Expressions and Equations

4.6 Formulas

CHAPTER SUMMARY

Key Points of Chapter 4

Chapter 4 Review Exercises

Chapter 4 Test

Cumulative Review of Chapters 1—4

**5. Linear Equations in Two Variables**

5.1 Graphing Linear Equations

5.2 Finding Linear Equations

5.3 Finding Equations of Linear Models

5.4 Using Linear Equations to Make Estimates and Predictions

5.5 Solving Linear Inequalities in One Variable

Taking it to the Lab: Climate Change Lab * Rope Lab * Shadow

Lab * Linear Equation Lab: Topic of Your Choice

CHAPTER SUMMARY

Key Points of Chapter 5

Chapter 5 Review Exercises

Chapter 5 Test

**6. Systems of Linear Equations**

6.1 Using Graphs and Tables to Solve Systems

6.2 Using Substitution to Solve Systems

6.3 Using Elimination to Solve Systems

6.4 Using Systems to Model Data

6.5 Perimeter, Value, Interest, and Mixture Problems

6.6 Linear Inequalities in Two Variables; Systems of Linear

Inequalities in Two Variables

Taking it to the Lab: Climate Change Lab

CHAPTER SUMMARY

Key Points of Chapter 6

Chapter 6 Review Exercises

Chapter 6 Test

Cumulative Review of Chapters 1—6

**7. Polynomials**

7.1 Graphing Quadratic Equations

7.2 Quadratic Models

7.3 Adding and Subtracting Polynomials

7.4 Multiplying Polynomials

7.5 Powers of Polynomials; Product of Binomial Conjugates

7.6 Properties of Exponents

7.7 Negative-Integer Exponents

7.8 Dividing Polynomials

Taking it to the Lab: Climate Change Lab * Projectile Lab

CHAPTER SUMMARY

Key Points of Chapter 7

Chapter 7 Review Exercises

Chapter 7 Test

**8. Factoring Polynomials and Solving Polynomial Equations**

8.1 Factoring Trinomials of the Form *x ^{2} + bx + c* and Differences of Two Squares

8.2 Factoring Out the GCF; Factoring by Grouping

8.3 Factoring Trinomials of the Form *ax ^{2} + bx + c*

8.4 Sums and Differences of Cubes; A Factoring Strategy

8.5 Solving Polynomial Equations

8.6 Using Factoring to Make Predictions with Quadratic Models

CHAPTER SUMMARY

Key Points of Chapter 8

Chapter 8 Review Exercises

Chapter 8 Test

Cumulative Review of Chapters 1—8

**9. Solving Quadratic Equations**

9.1 Simplifying Radical Expressions

9.2 Simplifying More Radical Expressions

9.3 Solving Quadratic Equations by the Square Root Property; The Pythagorean Theorem

9.4 Solving Quadratic Equations by Completing the Square

9.5 Solving Quadratic Equations by the Quadratic Formula

9.6 More Quadratic Models

Taking it to the Lab: Climate Change Lab * Projectile Lab

CHAPTER SUMMARY

Key Points of Chapter 9

Chapter 9 Review Exercises

Chapter 9 Test

**10. Rational Expressions and Equations**

10.1 Simplifying Rational Expressions

10.2 Multiplying and Dividing Rational Expressions; Converting Units

10.3 Adding Rational Expressions

10.4 Subtracting Rational Expressions

10.5 Solving Rational Equations

10.6 Proportions; Similar Triangles

10.7 Variation

10.8 Simplifying Complex Rational Expressions

Taking it to the Lab: Climate Change Lab * Estimating p Lab

CHAPTER SUMMARY

Key Points of Chapter 10

Chapter 10 Review Exercises

Chapter 10 Test

**11. More Radical Expressions and Equations**

11.1 Adding and Subtracting Radical Expressions

11.2 Multiplying Radical Expressions

11.3 Solving Square Root Equations

CHAPTER SUMMARY

Key Points of Chapter 11

Chapter 11 Review Exercises

Chapter 11 Test

Cumulative Review of Chapters 1—11

**A. Using a TI-83 or TI-84 Graphing Calculator**

A.1 Turning a Graphing Calculator On or Off

A.2 Making the Screen Lighter or Darker

A.3 Entering an Equation

A.4 Graphing an Equation

A.5 Tracing a Curve without a Scattergram

A.6 Zooming

A.7 Setting the Window Format

A.8 Plotting Points in a Scattergram

A.9 Tracing a Scattergram

A.10 Graphing Equations with a Scattergram

A.11 Tracing a Curve with a Scattergram

A.12 Turning a Plotter On or Off

A.13 Creating a Table

A.14 Creating a Table for Two Equations

A.15 Using “Ask” in a Table

A.16 Plotting Points in Two Scattergrams

A.17 Finding the Intersection Point(s) of Two Curves

A.18 Finding the Minimum or Maximum of a Curve

A.19 Finding any x-Intercepts of a Curve

A.20 Turning an Equation On or Off

A.21 Finding Coordinates of Points

A.22 Entering an Equation by Using Yn References

A.23 Responding to Error Messages

Answers to odd-numbered exercises

Index

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