There are many different ways that a polynomial equation can be represented. For example, a quadratic equation can be written in polynomial form or in vertex form.

Two quadratic equations in polynomial form and vertex form

patchwork quilt in which a square is completed from component parts
In this lesson, you will investigate one way that you can transform a quadratic equation or a quadratic expression in standard polynomial form into vertex form, which is written with a binomial that is squared. That method is called completing the square. As you move through the sections of this lesson, you will investigate and discover why the method is called completing the square. You will also examine some of the different ways that this method can prove to be extremely useful.