viii CONTENTS 1.2 Applications and Modeling with Linear Equations 112 Solving Applied Problems ■ Geometry Problems ■ Motion Problems ■ Mixture Problems ■ Modeling with Linear Equations 1.3 Complex Numbers 123 Basic Concepts of Complex Numbers ■ Operations on Complex Numbers 1.4 Quadratic Equations 131 The Zero-Factor Property ■ The Square Root Property ■ Completing the Square ■ The Quadratic Formula ■ Solving for a Specified Variable ■ The Discriminant Chapter 1 Quiz (Sections 1.1–1.4) 141 1.5 Applications and Modeling with Quadratic Equations 142 Geometry Problems ■ The Pythagorean Theorem ■ Height of a Projected Object ■ Modeling with Quadratic Equations 1.6 OtherTypes of Equations and Applications 154 Rational Equations ■ Work Rate Problems ■ Equations with Radicals ■ Equations with Rational Exponents ■ Equations Quadratic in Form Summary Exercises on Solving Equations 167 1.7 Inequalities 168 Linear Inequalities ■ Three-Part Inequalities ■ Quadratic Inequalities ■ Rational Inequalities 1.8 Absolute Value Equations and Inequalities 180 Basic Concepts ■ Absolute Value Equations ■ Absolute Value Inequalities ■ Special Cases ■ Absolute Value Models for Distance and Tolerance Test Prep 188 ■ Review Exercises 193 ■ Test 199 2 Graphs and Functions 201 2.1 Rectangular Coordinates and Graphs 202 Ordered Pairs ■ The Rectangular Coordinate System ■ The Distance Formula ■ The Midpoint Formula ■ Equations in Two Variables 2.2 Circles 213 Center-Radius Form ■ General Form ■ An Application 2.3 Functions 221 Relations and Functions ■ Domain and Range ■ Determining Whether Relations Are Functions ■ Function Notation ■ Increasing, Decreasing, and Constant Functions 2.4 Linear Functions 238 Basic Concepts of Linear Functions ■ Standard Form Ax + By = C ■ Slope ■ Average Rate of Change ■ Linear Models Chapter 2 Quiz (Sections 2.1–2.4) 252
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