Idiot's Guides: Algebra II PDF
Preview Idiot's Guides: Algebra II
No one likes a know-it-all. Most of us realize there’s no such thing—how could there be? The world is far too complicated for someone to understand everything there is to know. So when you come across a know-it-all, you smile to yourself as they ramble on because you know better. You understand that the quest for knowledge is a never-ending one, and you’re okay with that. You have no desire to know everything, just the next thing. You know what you don’t know, you’re confident enough to admit it, and you’re motivated to do something about it. At Idiot’s Guides, we, too, know what we don’t know, and we make it our business to find out. We find really smart people who are experts in their fields and then we roll up our sleeves and get to work, asking lots of questions and thinking long and hard about how best to pass along their knowledge to you in the easiest, most-accessible way possible. After all, that’s our promise—to make whatever you want to learn “As Easy as It Gets.” That means giving you a well-organized design that seamlessly and effortlessly guides you from page to page, topic to topic. It means controlling the pace you’re asked to absorb new information—not too much at once but just what you need to know right now. It means giving you a clear progression from easy to more difficult. It means giving you more instructional steps wherever necessary to really explain the details. And it means giving you fewer words and more illustrations wherever it’s better to show rather than tell. So here you are, at the start of something new. The next chapter in your quest. It can be an intimidating place to be, but you’ve been here before and so have we. Clear your mind and turn the page. By the end of this book, you won’t be a know-it-all, but your world will be a little less complicated than it was before. And we’ll be sure your journey is as easy as it gets. Mike Sanders Publisher, Idiot’s Guides Publisher: Mike Sanders Associate Publisher: Billy Fields Executive Acquisitions Editor: Lori Hand Development Editor: Kayla Dugger Cover Designer: Laura Merriman Book Designer: William Thomas Production Editor: Jana M. Stefanciosa Compositor: Brian Massey Proofreader: Laura Caddell Indexer: Brad Herriman PRODUCTION, LONDON Digital Producer: Alex Valizadeh Senior Digital Producer: Miguel Cunha DIGITAL OPERATIONS, DELHI Head of Digital Operations: Manjari Hooda Producer: Rahul Kumar Assistant Editor: Etika Kapil Operations Assistant: Tauhid Nasir First American Edition, 2015 Published in the United States by DK Publishing 6081 E. 82nd Street, Indianapolis, Indiana 46250 Copyright © 2015 Dorling Kindersley Limited A Penguin Random House Company 15 16 17 18 10 9 8 7 6 5 4 3 2 1 001–285170–November/2015 All rights reserved. Without limiting the rights under the copyright reserved above, no part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior written permission of the copyright owner. Published in the United States by Dorling Kindersley Limited. IDIOT’S GUIDES and Design are trademarks of Penguin Random House LLC eISBN: 9781615648696 Library of Congress Catalog Card Number: 2015937087 Note: This publication contains the opinions and ideas of its author. It is intended to provide helpful and informative material on the subject matter covered. It is sold with the understanding that the author and publisher are not engaged in rendering professional services in the book. If the reader requires personal assistance or advice, a competent professional should be consulted. The author and publisher specifically disclaim any responsibility for any liability, loss, or risk, personal or otherwise, which is incurred as a consequence, directly or indirectly, of the use and application of any of the contents of this book. Trademarks: All terms mentioned in this book that are known to be or are suspected of being trademarks or service marks have been appropriately capitalized. Alpha Books, DK, and Penguin Random House LLC cannot attest to the accuracy of this information. Use of a term in this book should not be regarded as affecting the validity of any trademark or service mark. DK books are available at special discounts when purchased in bulk for sales promotions, premiums, fund-raising, or educational use. For details, contact: DK Publishing Special Markets, 345 Hudson Street, New York, New York 10014 or [email protected]. Printed and bound in the United States idiotsguides.com Contents Part 1: Foundations 1 Building Blocks from Algebra I The Real Numbers Simplifying Expressions Order of Operations Example Order of Operations with Variables Solving Equations and Inequalities Linear Equations Linear Inequalities Graphing Lines Slope Finding the Points for a Line Writing a Linear Equation FOIL and Factoring Factoring a Quadratic Trinomial Factoring When the Coefficient of x2 Isn’t 1 2 Functions Relations and Functions Function Notation Building New Functions Function Arithmetic Composition Inverses Parent Functions and Transformations Rigid Transformations Nonrigid Transformations Creating Families of Functions Part 2: Linear Relationships 3 Linear Functions Inequalities in Two Variables Graphing an Inequality in Slope-Intercept Form Graphing an Inequality in Standard Form Fitting Equations to Data Piecewise Functions Graphing a Piecewise Function A Well-Known Piecewise Function 4 Absolute Value Absolute Value Equations Absolute Value Inequalities How Absolute Value Inequalities Work Solving Absolute Value Inequalities Absolute Value Functions 5 Solving Systems Algebraically Systems of Equations Graphing Substitution Elimination Systems with Three Variables Using Substitution Using Elimination Systems of Inequalities Linear Programming 6 Systems and Matrices Matrices and Matrix Arithmetic Addition and Subtraction Multiplication Determinants Representing a System by Matrices Cramer’s Rule Solving Systems by Row Operations Solving Systems by Inverse Matrices Finding an Inverse Matrix Solving a System by Inverses Part 3: Quadratic Relationships 7 Roots and Radicals Rational Exponents Simplifying Radical Expressions Rationalizing More Complex Denominators Solving Radical Equations Graphing Radical Functions 8 Quadratics Quadratic Equations Square Root Method Completing the Square Quadratic Formula Complex Numbers and Their Arithmetic Graphing Quadratic Functions Quadratic Modeling 9 Conics Parabolas Vertex Form Equation Graphing a Parabola Circles Ellipses Standard Form Equation Graphing an Ellipse Hyperbolas Standard Form Equation Graphing a Hyperbola Quadratic Systems Part 4: Polynomial and Rational Functions 10 Polynomials Polynomial Equations and Functions Factors and Solutions Rational Zeros Theorem Descartes’ Rule of Signs Finding the Solutions Long Division Synthetic Division Polynomial Inequalities Graphs of Polynomial Functions 11 Rational Functions Rational Expressions and Their Arithmetic Simplifying Rational Expressions Adding and Subtracting Multiplying Rational Expressions Dividing by a Rational Expression Complex Fractions Solving Rational Equations Cross-Multiplying Multiplying Through How to Graph Rational Functions Domain Asymptotes Intercepts Part 5: Calculating and Counting 12 Exponential and Logarithmic Functions Logarithms Properties of Logarithms Expanding an Expression Condensing an Expression Solving Exponential Equations Powers of the Same Base Log of Both Sides Quadratic Form Solving Log Equations Log Equals Constant Log Equals Log How to Graph Exponential and Logarithmic Functions Growth and Decay 13 Probability
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