Question 158726
There are several ways to approach this. If you are familiar with derivatives. take the first derivative and solve for 0. 

If you prefer to plot and see

{{{graph(400,400,-10,10,-100,10, x^2-12x)}}}

If you want to use just an algebraic approach, note that the equation is in the form of a parabola. Then either use the formauls for the vertex or find the zeros and then follow the verticla line that is halfway between those two points. For this equatuon, the zeros can be found by solving for {{{0 = x^2-12x}}}
{{{0 = x(x-12)}}}
So there are zeros at x = 0 and  x=12. The point halfway between them is x=6. So the vertex is on the vertical line x=6. Solving yields {{{p(6) = 6^2 - 6*12}}}
{{{p(6) = 36 - 72}}}
{{{p(6) = -36}}}

All of the methods will get you to the answer x=6