Question 1021496
The cubic function has a local maximum (a=positive) or minimum (a is negative) at x=h.
The derivative of this function is 3a(x-h)^2, so the rate of change of the function is a quadratic, and at x=h the rate of change is 0, the same as the instantaneous rate of change of the quadratic function is 0 at the vertex.  The final graph shows what is happening at x=3 and y=4.  The last graph is negative a.
{{{graph(300,200,-10,10,-10,10,(x-3)^3+2)}}}
{{{graph(300,200,-10,10,-10,10,(x-3)^3+4)}}}
{{{graph(300,200,-2,4,-10,10,(x-3)^3+4)}}}
{{{graph(300,200,-10,10,-10,10,-(x-3)^3+4)}}}