Idiot's Guides: Algebra II

389 Pages·2015·75.96 MB·English

by  Wheater

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
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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

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First American Edition, 2015
Published in the United States by DK Publishing
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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