# Quadratic formula review

CCSS Math: HSA.REI.B.4, HSA.REI.B.4b

The quadratic formula allows us to solve any quadratic equation that's in the form ax^2 + bx + c = 0. This article reviews how to apply the formula.

## What is the quadratic formula?

The quadratic formula says that

for any quadratic equation like:

### Example

We're given an equation and asked to solve for $q$:

This equation is already in the form $ax^2 + bx + c = 0$, so we can apply the quadratic formula where $a = -7, b = 2, c = 9$:

Let's check both solutions to be sure it worked:

$q=-1$ | $q=\dfrac{9}{7}$ |
---|---|

$\begin{aligned}0&=-7q^2+2q+9\\\\0&=-7(-1)^2+2(-1)+9 \\\\0&=-7(1)-2+9 \\\\0&=-7-2+9\\\\0&=0\end{aligned}$ | $\begin{aligned}0&=-7q^2+2q+9\\\\0&=-7\left(\dfrac{9}{7}\right)^2+2\left (\dfrac{9}{7}\right)+9 \\\\0&=-7\left(\dfrac{81}{49}\right)+\left (\dfrac{18}{7}\right)+9 \\\\0&=-\left(\dfrac{81}{7}\right)+\left (\dfrac{18}{7}\right)+9 \\\\0&=-\left(\dfrac{63}{7}\right) +9 \\\\0&=-9 +9 \\\\0&=0\end{aligned}$ |

Yep, both solutions check out.

*Want to learn more about the quadratic formula? Check out this video.*

*Want more practice? Check out this exercise*.