Question 117324
A parabola is symmetric about the vertex. 
If you take the average of the x intercepts you will find the x coordinate of the parabola.
{{{x[v]=(1+5)/2}}}
{{{x[v]=3}}}
The general equation, congruent to {{{y=x^2}}}, is then, 
{{{y=(x-3)^2+y[0]}}}
Find {{{y[0]}}} by using either point, 
{{{0=(5-3)^2+y[0]}}}
{{{y[0]=-4}}}
{{{y=(x-3)^2-4}}}
The vertex is (3,-4).
{{{ graph( 300, 300, -10, 10, -10, 10, x^2, (x-3)^2-4) )}}}