# 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.
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In this topic, we'll analyze, graph and solve 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!

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!

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!