The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ The quadratic formula gives the solutions of a [[quadratic equation]]. Note that because of the $\pm$ term, there will be two solutions. Discard solutions that are not within the domain of your problem. The quantity $b^2 - 4ac$ is called the **discriminant** and gives useful information about the solution. If the discriminant is positive, there are two real solutions. If it is zero, there is one real solution. If it is negative, there are no real solutions. The quadratic formula can be used for the purposes of graphing by hand or finding a [[function maximum]].