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Algebra II For Dummies, 2nd Edition (9781119543145) was previously published as Algebra II For Dummies, 2nd Edition (9781119090625). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.





Your complete guide to acing Algebra II


Do quadratic equations make you queasy? Does the mere thought of logarithms make you feel lethargic? You're not alone! Algebra can induce anxiety in the best of us, especially for the masses that have never counted math as their forte. But here's the good news: you no longer have to suffer through statistics, sequences, and series alone. Algebra II For Dummies takes the fear out of this math course and gives you easy-to-follow, friendly guidance on everything you'll encounter in the classroom and arms you with the skills and confidence you need to score high at exam time.


Gone are the days that Algebra II is a subject that only the serious 'math' students need to worry about. Now, as the concepts and material covered in a typical Algebra II course are consistently popping up on standardized tests like the SAT and ACT, the demand for advanced guidance on this subject has never been more urgent. Thankfully, this new edition of Algebra II For Dummies answers the call with a friendly and accessible approach to this often-intimidating subject, offering you a closer look at exponentials, graphing inequalities, and other topics in a way you can understand.





Examine exponentials like a pro

Find out how to graph inequalities

Go beyond your Algebra I knowledge

Ace your Algebra II exams with ease



Whether you're looking to increase your score on a standardized test or simply succeed in your Algebra II course, this friendly guide makes it possible.

Algebra II For Dummies, 2nd Edition

Introduction 1





About This Book 1





Foolish Assumptions 2





Icons Used in This Book 3





Beyond the Book 4





Where to Go from Here 4





Part 1: Homing in on Basic Solutions 5





Chapter 1: Going Beyond Beginning Algebra 7





Outlining Algebraic Properties 8





Keeping order with the commutative property 8





Maintaining group harmony with the associative property 9





Distributing a wealth of values 9





Checking out an algebraic ID 10





Singing along in-verses 11





Ordering Your Operations 11





Zeroing in on the Multiplication Property of Zero 12





Expounding on Exponential Rules 13





Multiplying and dividing exponents 13





Getting to the roots of exponents 14





Raising or lowering the roof with exponents 14





Making nice with negative exponents 15





Implementing Factoring Techniques 15





Factoring two terms 16





Taking on three terms 17





Factoring four or more terms by grouping 19





Chapter 2: Toeing the Straight Line: Linear Equations 21





Linear Equations: Handling the First Degree 21





Tackling basic linear equations 22





Clearing out fractions 23





Isolating different unknowns 24





Linear Inequalities: Algebraic Relationship Therapy 25





Solving linear inequalities 26





Introducing interval notation 27





Compounding inequality issues 28





Absolute Value: Keeping Everything in Line 30





Solving absolute value equations 31





Seeing through absolute value inequality 31





Chapter 3: Conquering Quadratic Equations 35





Implementing the Square Root Rule 36





Dismantling Quadratic Equations into Factors 37





Factoring binomials 37





Factoring trinomials 39





Factoring by grouping 40





Resorting to the Quadratic Formula 41





Finding rational solutions 42





Straightening out irrational solutions 42





Formulating huge quadratic results 43





Completing the Square: Warming Up for Conics 43





Squaring up a quadratic equation 44





Completing the square twice over 45





Tackling Higher-Powered Polynomials 46





Handling the sum or difference of cubes 47





Tackling quadratic-like trinomials 48





Solving Quadratic Inequalities 49





Keeping inequality strictly quadratic 50





Signing up for fractions 52





Increasing the number of factors 53





Considering absolute value inequalities 53





Chapter 4: Rooting Out the Rational, Radical, and Negative 55





Acting Rationally with Fraction-Filled Equations 56





Systematically solving rational equations 56





Solving rational equations with proportions 60





Ridding Yourself of a Radical 61





Squaring both sides of a radical equation 62





Calming two radicals 63





Changing Negative Attitudes about Exponents 65





Flipping negative exponents out of the picture 65





Factoring out negatives to solve equations 66





Fooling Around with Fractional Exponents 68





Combining terms with fractional exponents 69





Factoring fractional exponents 69





Solving equations by working with fractional exponents 70





Chapter 5: Graphing Your Way to the Good Life 73





Coordinating Your Graphing Efforts 74





Identifying the parts of the coordinate plane 74





Plotting from dot to dot 75





Streamlining the Graphing Process with Intercepts and Symmetry 76





Finding x- and y-intercepts 77





Reflecting on a graph's symmetry 78





Graphing Lines 80





Finding the slope of a line 81





Facing two types of equations for lines 82





Identifying parallel and perpendicular lines 85





Looking at 10 Basic Forms 86





Lines and quadratics 86





Cubics and quartics 87





Radicals and rationals 87





Exponential and logarithmic curves 88





Absolute values and circles 89





Solving Problems with a Graphing Calculator 89





Entering equations into graphing calculators correctly 90





Looking through the graphing window 92





Part 2: Facing Off with Functions 95





Chapter 6: Formulating Function Facts 97





Defining Functions 98





Introducing function notation 98





Evaluating functions 98





Homing In on Domain and Range 99





Determining a function's domain 99





Describing a function's range 100





Betting on Even or Odd Functions 102





Recognizing even and odd functions 102





Applying even and odd functions to graphs 103





Facing One-to-One Confrontations 104





Defining one-to-one functions 104





Eliminating one-to-one violators 105





Going to Pieces with Piecewise Functions 106





Doing piecework 107





Applying piecewise functions 108





Composing Yourself and Functions 110





Performing compositions 110





Simplifying the difference quotient 111





Singing Along with Inverse Functions 112





Determining if functions are inverses 112





Solving for the inverse of a function 113





Chapter 7: Sketching and Interpreting Quadratic Functions 115





Interpreting the Standard Form of Quadratics 116





Starting with "a" in the standard form 116





Following up with "b" and "c" 117





Investigating Intercepts in Quadratics 118





Finding the one and only y-intercept 119





Finding the x-intercepts 120





Going to the Extreme: Finding the Vertex 123





Lining Up along the Axis of Symmetry 124





Sketching a Graph from the Available Information 125





Applying Quadratics to the Real World 127





Selling candles 127





Shooting basketballs 128





Launching a water balloon 130





Chapter 8: Staying Ahead of the Curves: Polynomials 133





Taking a Look at the Standard Polynomial Form 134





Exploring Polynomial Intercepts and Turning Points 134





Interpreting relative value and absolute value 135





Counting intercepts and turning points 135





Solving for polynomial intercepts 138





Determining Positive and Negative Intervals 139





Using a sign-line 140





Interpreting the rule 141





Finding the Roots of a Polynomial 143





Factoring for polynomial roots 143





Saving your sanity: The Rational Root Theorem 145





Letting Descartes make a ruling on signs 148





Synthesizing Root Findings 150





Using synthetic division to test for roots 150





Synthetically dividing by a binomial 153





Wringing out the Remainder (Theorem) 154





Chapter 9: Reasoning with Rational Functions 157





Exploring Rational Functions 158





Sizing up domain 158





Introducing intercepts 159





Adding Asymptotes to the Rational Pot 160





Determining the equations of vertical asymptotes 160





Determining the equations of horizontal asymptotes 161





Graphing vertical and horizontal asymptotes 161





Crunching the numbers and graphing oblique asymptotes 163





Accounting for Removable Discontinuities 164





Removal by factoring 164





Evaluating the removal restrictions 165





Showing removable discontinuities on a graph 165





Pushing the Limits of Rational Functions 167





Evaluating limits at discontinuities 168





Going to infinity 170





Catching rational limits at infinity 172





Putting It All Together: Sketching Rational Graphs from Clues 173





Chapter 10: Exposing Exponential and Logarithmic Functions 177





Evaluating Exponential Expressions 178





Exponential Functions: It's All about the Base, Baby 179





Observing the trends in bases 179





Meeting the most frequently used bases: 10 and e 180





Solving Exponential Equations 182





Making bases match 182





Recognizing and using quadratic patterns 184





Showing an "Interest" in Exponential Functions 186





Applying the compound interest formula 186





Looking at continuous compounding 188





Logging On to Logarithmic Functions 189





Meeting the properties of logarithms 190





Putting your logs to work 191





Solving Logarithmic Equations 193





Setting log equal to log 194





Rewriting log equations as exponentials 195





Graphing Exponential and Logarithmic Functions 196





Expounding on the exponential 196





Not seeing the logs for the trees 198





Part 3: Conquering Conics and Systems of Equations 203





Chapter 11: Cutting Up Conic Sections 205





Cutting Up a Cone 206





Opening Every Which Way with Parabolas 206





Looking at parabolas with vertices at the origin 207





Observing the general form of parabola equations 210





Sketching the graphs of parabolas 211





Converting parabolic equations to the standard form 214





Going Round and Round in Conic Circles 215





Standardizing the circle 215





Specializing in circles 217





Preparing Your Eyes for Solar Ellipses 218





Raising the standards of an ellipse 218





Sketching an elliptical path 221





Feeling Hyper about Hyperbolas 222





Including the asymptotes 223





Graphing hyperbolas 224





Identifying Conics from Their Equations, Standard or Not 227





Chapter 12: Solving Systems of Linear Equations 229





Looking at the Standard Linear-Systems Form and Its Possible Solutions 230





Graphing Solutions of Linear Systems 230





Pinpointing the intersection 231





Toeing the same line twice 232





Dealing with parallel lines 232





Solving Systems of Two Linear Equations by Using Elimination 233





Getting to the point with elimination 234





Recognizing solutions indicating parallel or coexisting lines 235





Making Substitution the Choice 236





Variable substituting made easy 236





Identifying parallel and coexisting lines 237





Using Cramer's Rule to Defeat Unwieldy Fractions 238





Setting up the linear system for Cramer 239





Applying Cramer's Rule to a linear system 240





Tackling Linear Systems with Three Linear Equations 241





Solving three-equation systems with algebra 241





Generalizing multiple solutions for linear equations 243





Upping the Ante with Larger Systems 244





Applying Linear Systems to Our 3-D World 247





Using Systems to Decompose Fractions 248





Chapter 13: Solving Systems of Nonlinear Equations and Inequalities 251





Crossing Parabolas with Lines 252





Determining the point(s) where a line and parabola cross paths 253





Dealing with a solution that's no solution 254





Intertwining Parabolas and Circles 255





Managing multiple intersections 256





Sorting out the solutions 258





Planning Your Attack on Other Systems of Equations 260





Mixing polynomials and lines 260





Crossing polynomials 261





Navigating exponential intersections 263





Rounding up rational functions 265





Playing Fair with Inequalities 268





Drawing and quartering inequalities 268





Graphing areas with curves and lines 269





Part 4: Shifting into High Gear with Advanced Concepts 271





Chapter 14: Simplifying Complex Numbers in a Complex World 273





Using Your Imagination to Simplify Powers of i 274





Understanding the Complexity of Complex Numbers 275





Operating on complex numbers 276





Multiplying by the conjugate to perform division 277





Simplifying radicals 279





Solving Quadratic Equations with Complex Solutions 280





Working Polynomials with Complex Solutions 282





Identifying conjugate pairs 283





Interpreting complex zeros 283





Chapter 15: Making Moves with Matrices 287





Describing the Different Types of Matrices 288





Row and column matrices 289





Square matrices 289





Zero matrices 289





Identity matrices 289





Performing Operations on Matrices 290





Adding and subtracting matrices 290





Multiplying matrices by scalars 291





Multiplying two matrices 291





Applying matrices and operations 293





Defining Row Operations 297





Finding Inverse Matrices 298





Determining additive inverses 299





Determining multiplicative inverses 299





Dividing Matrices by Using Inverses 304





Using Matrices to Find Solutions for Systems of Equations 305





Chapter 16: Making a List: Sequences and Series 307





Understanding Sequence Terminology 308





Using sequence notation 308





No-fear factorials in sequences 309





Alternating sequential patterns 309





Looking for sequential patterns 310





Taking Note of Arithmetic and Geometric Sequences 313





Finding common ground: Arithmetic sequences 313





Taking the multiplicative approach: Geometric sequences 315





Recursively Defining Functions 317





Making a Series of Moves 318





Introducing summation notation 318





Summing arithmetically 319





Summing geometrically 320





Applying Sums of Sequences to the Real World 323





Stacking the blocks 323





Negotiating your allowance 323





Bouncing a ball 324





Highlighting Special Formulas 326





Chapter 17: Everything You Wanted to Know about Sets 329





Revealing Set Notation 329





Listing elements with a roster 330





Building sets from scratch 330





Going for all (universal set) or nothing (empty set) 331





Subbing in with subsets 331





Operating on Sets 333





Celebrating the union of two sets 333





Looking both ways for set intersections 334





Feeling complementary about sets 335





Counting the elements in sets 335





Drawing Venn You Feel Like It 336





Applying the Venn diagram 337





Using Venn diagrams with set operations 338





Adding a set to a Venn diagram 339





Focusing on Factorials 342





Making factorial manageable 342





Simplifying factorials 343





How Do I Love Thee? Let Me Count Up the Ways 344





Applying the multiplication principle to sets 344





Arranging permutations of sets 345





Mixing up sets with combinations 348





Branching Out with Tree Diagrams 350





Picturing a tree diagram for a permutation 351





Drawing a tree diagram for a combination 352





Part 5: The Part of Tens 353





Chapter 18: Ten Multiplication Tricks 355





Squaring Numbers That End in 5 355





Finding the Next Perfect Square 356





Recognizing the Pattern in Multiples of 9 and 11 357





Casting Out 9s 357





Casting Out 9s: The Multiplication Moves 358





Multiplying by 11 359





Multiplying by 5 360





Finding Common Denominators 361





Determining Divisors 362





Multiplying Two-Digit Numbers 362





Chapter 19: Ten Special Types of Numbers 365





Triangular Numbers 365





Square Numbers 366





Hexagonal Numbers 366





Perfect Numbers 367





Amicable Numbers 367





Happy Numbers 368





Abundant Numbers 368





Deficient Numbers 368





Narcissistic Numbers 368





Prime Numbers 369





Index 371