# What is the extreme value of a quadratic function?

A quadratic function $f \left(x\right) = a {x}^{2} + b x + c$ has an extreme value at its vertex, so if $a > 0$, then $f \left(- \frac{b}{a}\right)$ is the maximum, and if $a < 0$, then $f \left(- \frac{b}{a}\right)$ is the minimum.