smc

The minimum value of this parabola is found at its turning point, on the line $\boxed{x=\frac{-p}{2}}$. Indeed, the turning point of any function of the form $a{x}^2+bx+c$ has an x-coordinate of $\frac{-b}{2a}$. This can be seen at the average of the quadratic's two roots (whose sum is $\frac{-b}{a}$) or (using calculus) as the value of its derivative set equal to $0$.