If you have taken algebra 2, you know you can write quadratic functions in three forms:

- Standard form:
- Vertex form:
- Factored form:

No matter which of the forms you have, you are often asked to find the roots (x-intercepts). The factored form is already done for you: the roots are the values of and . If your equation is in standard form, you use the quadratic formula. But what do you do if you have a quadratic in vertex form? Most students are taught to expand the equation into standard form (and then use the quadratic formula). But there’s a quick shortcut that is pretty easy to use. In fact, you can write the roots by inspection. If , then the roots are

There are three cases:

- : There is one (double) root;
- have different signs: the two roots are real;
- have the same sign: the two roots are complex.

In the complex case, you can express the roots as

Here are two quick examples:

Example 1:

Using the formula above, the roots can be written immediately as

Example 2:

The roots are: