The quadratic function

Well, we know that a quadratic function is a MIN when the coefficient of x^2 is positive and a MAX when the coefficient of x^2 is negative. Is there a particular proof or derivation for this? What is the reasoning behind it?

Thanks in advance.

Let


For max or min put

..i.e

. If then is point of minima and if then is point of maxima

ALITER


Obviously, if
if