Algebra I

Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.
Community Questions

Introduction to algebra

Videos exploring why algebra was developed and how it helps us explain our world.

Linear equations

We will now equate two algebraic expressions and think about how it might constrain what value the variables can take on. The algebraic manipulation you learn here really is the heart of algebra.

Linear inequalities

Exploring a world where both sides aren't equal anymore!

Two-variable linear equations and introduction to functions

Learn all about linear equations and their graphs. Model real-world situations by writing linear equations and functions.


Functions are mathematical entities that assign unique outputs to given inputs. Sounds simple? Think again! In this topic you will evaluate, graph, analyze, and create various types of functions.


You may have worked with patterns in earlier grades, now it's time to move on to sequences! Did you know sequences are simply functions, defined over the whole numbers? In this topic you will learn about the explicit and the recursive definitions of sequences, and about arithmetic and geometric sequences. You will evaluate sequences, construct sequences, and model real-world situations with sequences.

Systems of linear equations

Learn how to interpret solutions to systems of linear equations and solve them.

Two-variable linear inequalities

In this topic, we study inequalities like x+2y>5 and graph them. This helps us see their solutions. We also explore systems of inequalities (multiple inequalities at the same time) and use them to describe real-world situations.

Introduction to polynomials and quadratic factorization

Learn how to add, subtract, multiply, and factor polynomial expressions.

Quadratic equations

In this topic, we'll analyze, graph and solve quadratic equations.

Expressions with rational exponents and radicals

Learn about expressions with rational exponents like x^(2/3), about radical expressions like √(2t^5), and about the relationship between these two forms of representation. Learn how to evaluate and simplify such expression.

Introduction to exponential functions

Learn how to construct, analyze, graph, and interpret basic exponential functions of the form f(x)=a*r^x.

Rational and irrational numbers

Learn about irrational numbers and how to identify them.


Quadratic equations

In this topic, we'll analyze, graph and solve quadratic equations.
Community Questions
All content in “Quadratic equations”

Solving quadratics by taking square root

Let's explore one of the most fundamental ways to solve a quadratic equation when it is already written in terms of a square of an expression in x--solve for the expression and take the square root. As we'll see, equations are not always in this form, and that is where completing the square--which puts equations in this form--is essential!

Solving quadratics by factoring

Just saying the word "quadratic" will make you feel smart and powerful. Try it. Imagine how smart and powerful you would actually be if you know what a quadratic is. Even better, imagine being able to completely dominate these "quadratics" with new found powers of factorization. Well, dream no longer. This tutorial will be super fun. Just bring to it your equation solving skills, your ability to multiply binomials and a non-linear way of thinking!

Completing the square

You're already familiar with factoring quadratics, but have begun to realize that it only is useful in certain cases. Well, this tutorial will introduce you to something far more powerful and general. Even better, it is the bridge to understanding and proving the famous quadratic formula. Welcome to the world of completing the square!

The quadratic formula (quadratic equation)

Probably one of the most famous tools in mathematics, the quadratic formula (a.k.a. quadratic equation) helps you think about the roots of ANY quadratic (even ones that have no real roots)! As you'll see, it is just the by-product of completing the square, but understanding and applying the formula will take your algebra skills to new heights. In theory, one could apply the quadratic formula in a brainless way without understanding factoring or completing the square, but that's lame and uninteresting. We recommend coming to this tutorial with a solid background in both of those techniques. Have fun!

Quadratic inequalities

You are familiar with factoring quadratic expressions and solving quadratic equations. Well, as you might guess, not everything in life has to be equal. In this short tutorial we will look at quadratic inequalities.