Processing math: 100%
Skip to main content
ORCCA
Open Resources for Community College Algebra
Portland Community College Faculty
Contents
Index
Prev
Up
Next
Annotations
Contents
Prev
Up
Next
Front Matter
Colophon
Acknowledgements
To All
Pedagogical Decisions
1
Basic Math Review
Arithmetic with Negative Numbers
Fractions and Fraction Arithmetic
Absolute Value and Square Root
Order of Operations
Set Notation and Types of Numbers
Comparison Symbols
Notation for Intervals
Chapter Review
2
Variables, Expressions, and Equations
Variables and Evaluating Expressions
Equations and Inequalities as True/False Statements
Solving One-Step Equations
Solving One-Step Inequalities
One-Step Equations With Percentages
Modeling with Equations and Inequalities
Introduction to Exponent Rules
Simplifying Expressions
Chapter Review
3
Linear Equations and Inequalities
Solving Multistep Linear Equations and Inequalities
Linear Equations and Inequalities with Fractions
Isolating a Linear Variable
Ratios and Proportions
Special Solution Sets
Chapter Review
4
Graphing Lines
Cartesian Coordinates
Graphing Equations
Exploring Two-Variable Data and Rate of Change
Slope
Slope-Intercept Form
Point-Slope Form
Standard Form
Horizontal, Vertical, Parallel, and Perpendicular Lines
Summary of Graphing Lines
Linear Inequalities in Two Variables
Graphing Lines Chapter Review
5
Systems of Linear Equations
Solving Systems of Linear Equations by Graphing
Substitution
Elimination
6
Polynomial Operations
Exponent Rules and Scientific Notation
Adding and Subtracting Polynomials
Multiplying Polynomials
Special Cases of Multiplying Polynomials
Dividing by a Monomial
7
Factoring
Factoring out the Common Factor
Factoring by Grouping
Factoring Trinomials with Leading Coefficient One
Factoring Trinomials with a Nontrivial Leading Coefficient
Factoring Special Polynomials
Factoring Strategies
8
Solving Quadratic Equations
Solving Quadratic Equations by Factoring
Square Root Properties
Solving Quadratic Equations by Using a Square Root
The Quadratic Formula
Complex Solutions to Quadratic Equations
Review of Solving Quadratic Equations
9
Graphs of Quadratic Functions
Introduction to Functions
Properties of Quadratic Functions
Graphing Quadratic Functions
10
Functions and Their Representations
Function Basics
Domain and Range
Using Technology to Explore Functions
Simplifying Expressions with Function Notation
Technical Definition of a Function
11
Absolute Value Functions
Introduction to Absolute Value Functions
Compound Inequalities
Absolute Value Equations and Inequalities
12
More on Quadratic Functions
Graphs and Vertex Form
Completing the Square
More on Complex Solutions to Quadratic Equations
Complex Number Operations
13
Rational Functions and Equations
Introduction to Rational Functions
Multiplication and Division of Rational Expressions
Addition and Subtraction of Rational Expressions
Complex Fractions
Solving Rational Equations
14
Radical Functions and Equations
Introduction to Radical Functions
Radical Expressions and Rational Exponents
More on Rationalizing the Denominator
Solving Radical Equations
Appendices
Geometry Basics
Arithmetic with Whole Numbers, Decimals, and Natural Exponents
PCC Course Content and Outcome Guides
Index
Authored in PreTeXt
Chapter
9
Graphs of Quadratic Functions
ΒΆ
9.1
Introduction to Functions
9.2
Properties of Quadratic Functions
9.3
Graphing Quadratic Functions