Chapter 4 - Applications of the Derivative - 4.1 Maxima and Minima - 4.1 Exercises - Page 244: 80

$x = \frac{−b}{2a}$.

Since a parabola either opens up and has a minimum at its vertex, or open down and has a maximum at its vertex, it will always have exactly one extreme value. We have $f'(x) = 2ax + b$, which is zero when $x = \frac{−b}{2a}$ , so that one critical point is the location of the vertex which gives the extreme point.