Interactive course — Foundational Math

Algebra II

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

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Overview

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.

Topics covered

  • Absolute Value
  • Asymptotes
  • Domain and Range
  • Exponents
  • Factoring Polynomials
  • Function Composition
  • Inverses of Functions
  • Piecewise Functions
  • Projectile Motion
  • Rational Functions
  • The Binomial Theorem
  • The Quadratic Formula

Interactive quizzes

39

Concepts and exercises

365+

Course map

Prerequisites and Next Steps

  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!

      1
    2. Transforming Functions

      Practice predicting the behavior of function transformations.

      2
    3. Factoring and Beyond

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

      3
  2. 2

    Function Fundamentals

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

    1. Function Notation

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

      4
    2. Playing With Functions

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

      5
    3. Domain and Range

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

      6
    4. So Many Functions

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

      7
  3. 3

    Transformations

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

    1. Shifts and Stretches

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

      8
    2. Symmetry

      Throw some negatives into the mix and see what happens!

      9
    3. Inverse Functions

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

      10
    4. Composition

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

      11
    5. Compositions as Transformations

      Explore the close connection between composing functions and applying internal function transformations.

      12
  4. 4

    Powers and Radicals

    Explore exponents and roots of all kinds.

    1. Powers

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

      13
    2. Zero and Negative Exponents

      What happens when the exponent is less than 1?

      14
    3. Fractional Exponents

      What happens when the exponent isn't an integer?

      15
    4. Radical Conjugates

      This simplification technique lets you move and remove radicals.

      16
    5. Infinite Nests

      Solve some unusual problems where the functions are defined as infinite compositions of square roots.

      17
  5. 5

    Polynomials

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

    1. Playing With Polynomials

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

      18
    2. Polynomial Graph Basics

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

      19
    3. Polynomial Symmetries

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

      20
    4. Projectile Motion

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

      21
    5. Polynomial Arithmetic

      Practice adding, subtracting, and multiplying polynomials.

      22
  6. 6

    Factoring Polynomials

    Split polynomials down to their smallest parts!

    1. Playing With Factored Form

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

      23
    2. Factoring Quadratic Polynomials

      Master the techniques for quadratic factoring!

      24
    3. More Factoring

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

      25
    4. The Quadratic Formula

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

      26
    5. Polynomial Long Division

      Learn how to divide by polynomials using a technique similar to what's used in arithmetic with numbers.

      27
    6. Polynomial Problem Solving

      Combine all of the techniques you've learned to tackle a variety of challenging polynomial problems.

      28
    7. The Binomial Theorem

      Learn how to apply Pascal's triangle to quickly expand binomials.

      29
  7. 7

    Rational Functions

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

    1. Direct and Inverse Variation

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

      30
    2. Direct and Inverse Variation With Powers

      Explore what variation looks like when larger powers are involved.

      31
    3. Asymptotic Behavior Part 1

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

      32
    4. Asymptotic Behavior Part 2

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

      33
    5. Problem Solving

      Combine all of the techniques you've learned so far to solve these rational function problems.

      34
  8. 8

    Piecewise Functions

    Make new functions by mashing together old ones.

    1. Absolute Value Introduction

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

      35
    2. Modeling Absolute Value Scenarios

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

      36
    3. Absolute Value Problem Solving

      Practice and strengthen your skills by solving some challenging absolute value problems.

      37
    4. Piecewise Functions

      Create Frankenstein functions out of the pieces of spliced-up common functions!

      38
    5. Floor and Ceiling

      Explore functions defined by the operation of rounding down or up to the nearest integer.

      39