## 2.2 Understanding Graphs

Supercharge your thinking with the language of algebra.

Seeing Solutions

Practice Seeing Solutions

Graphing Solutions

Practice Graphing Solutions

Revealing Patterns

Practice Revealing Patterns

Choosing Values

Practice Choosing Values

Continuity

Practice Continuity

Using Continuity

Practice Using Continuity

Diminishing Returns

Intercepts

Practice Intercepts

Up and Down

Practice Up and Down

Minimums and Maximums

Practice Minimums and Maximums

Bounded Graphs

Practice Bounded Graphs

Graphs with Gaps

Practice Graphs with Gaps

Training an AI

Rate of Change

Practice Rate of Change

Slope and Parameters

Practice Slope and Parameters

The y-Intercept

Practice The y-Intercept

Horizontal and Vertical Lines

Practice Horizontal and Vertical Lines

Rules of Thumb

Multiplying Expressions

Practice Multiplying Expressions

Quadratic Equations

Practice Quadratic Equations

Symmetry

Practice Symmetry

Shifting Parabolas

Practice Shifting Parabolas

Wide, Narrow, and Upside Down

Practice Wide, Narrow, and Upside Down

Building Quadratics

Practice Building Quadratics

Optimizing Revenue

Population Growth

### Course description

This course explores the twin pillars of algebraic thinking—equations and graphs. With these two tools, we'll unpack algebra's big ideas and develop a powerful perspective to solve its essential problems. By the end of this course, you'll understand graphs and their relationship to the equations they represent, enabling you to answer questions involving equations even when it's impossible to solve them by hand. Though a familiarity with solving equations is helpful, we'll start with a review of the basics and build on them throughout the course. When you finish, you'll be ready to conquer a wide range of algebraic techniques in Algebra 1.

### Topics covered

- Algebraic Expressions
- Coordinate Plane
- Equations
- Graphs
- Linear Equations
- Ordered Pairs
- Rates
- Simplifying
- Systems of Equations
- Variables

### Prerequisites and next steps

Though a familiarity with solving equations is helpful, we'll start with a review of the basics and build on them throughout the course.

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### 3.1 Measurement

Start exploring geometry with an intuitive introduction to the essentials.

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