So far in Algebra 1 you will have only dealt with equations that use variables to the first power. That is, you haven’t had to deal with any equations that use variables that have an exponent. That’s about to change as you start to deal with quadratic equations, which involve polynomials of just one variable with the variable raised to the second power. The following are some examples of quadratic polynomials:

All of these polynomials have only one variable, and their variable is raised to the second power. That’s what makes them quadratic.

When we dealt with linear equations, we had a basic form for writing out the equation. That form was y = mx + b. For quadratics, we have standard form as well, and it looks like this:

Before you do anything with a quadratic equation, you’re going to need to put it into this form. Here we’re going to look at an example of putting a quadratic equation into the standard form for practice and to show you what the process looks like.

Let’s move everything to the left side of the equation.

And now we have it in the regular form.

When we graph quadratic equations, we’re going to get a shape that has a bit of a curve to it. This shape is called a parabola.

A neat feature of quadratic equations is that they can have zero, one, or two real solutions. For example, here are three equations:

In the first equation, x = 3 is the only solution. In the second equation, y = -1 and y = -3 are both solutions. In the final equation, there are no real solutions.