Algebra II

Play and experiment with interactive graphs to build a strong foundation in algebra!

Use interactive graphing apps to explore and transform functions of all varieties: polynomials, exponents, logarithms, absolute value, and more. Learn a method of factoring not commonly taught in school, practice modeling scenarios, and do problem solving that reveals the beauty of mathematics.

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1. 1

Introduction

Use experiments and play with graphs to learn algebra!

1. Modeling and Functions

Interact with functions by sliding their variables higher and lower to see what happens!

2. Transforming Functions

Practice predicting the behavior of function transformations.

3. Factoring and Beyond

Explore factoring polynomials from a new perspective, and learn a new factoring technique.

2. 2

Function Fundamentals

Function notation, domain, range, and a plethora of graph types.

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Function Notation

Review the definition of "function" and the notation used to represent functions.

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Playing With Functions

Explore a variety of function types by experimenting and playing with their graphs.

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Domain and Range

Learn how the domains and ranges of functions depend on each other — and on the function types.

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So Many Functions

Strengthen your skills working with quadratic, cubic, exponential, and trigonometric functions.

3. 3

Transformations

Move any function around or change its shape with a fixed set of rules.

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Shifts and Stretches

How can a function wind up stretched and transposed up, down, left, or right on the plane?

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Symmetry

Throw some negatives into the mix and see what happens!

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Inverse Functions

What happens when the input becomes the output and the output becomes the input?

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Composition

First apply one function and then another, how does the initial input relate to the final output?

4. 4

Explore exponents and roots of all kinds.

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Powers

Explore a fast-growing power function used to model growth in finance and biology.

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Zero and Negative Exponents

What happens when the exponent is less than 1?

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Fractional Exponents

What happens when the exponent isn't an integer?

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This simplification technique lets you move and remove radicals.

5. 5

Polynomials

Here you'll find every degree from zero to infinity.

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Playing With Polynomials

Get a feel for how polynomials work by interacting with their graphs.

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Polynomial Graph Basics

Solidify your understanding of how the graphs of polynomials are related to their functions.

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Polynomial Symmetries

Sometimes a bit of reflection can make things a lot easier.

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Projectile Motion

Apply quadratics to study and draw conclusions about these flying and falling objects!

6. 6

Factoring Polynomials

Split polynomials down to their smallest parts!

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Playing With Factored Form

Explore the art of factoring polynomials from new, graphical perspectives.

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Master the techniques for quadratic factoring!

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More Factoring

Expand your factoring skills to cover cases where the leading coefficient is greater than 1.

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Apply one of the most famous formulas in early mathematics to factor some polynomials.

7. 7

Rational Functions

Put together two polynomials with division, and a new world opens up.

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Direct and Inverse Variation

When one variable goes up, does the other go up with it?

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Direct and Inverse Variation With Powers

Explore what variation looks like when larger powers are involved.

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Asymptotic Behavior Part 1

Get closer and closer and closer... to infinity.

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Asymptotic Behavior Part 2

Learn how to tackle these tricky horizontal and slant asymptote cases!

8. 8

Piecewise Functions

Make new functions by mashing together old ones.

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Absolute Value Introduction

What are absolute value functions and how does arithmetic interact with them?

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Modeling Absolute Value Scenarios

Consider some real-life scenarios where the concept of absolute value applies.

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