Question 144632
For our vertex, the equation's formula is:
{{{(x-3)^2=4p(y-2.5)}}}

(4, 5.5) is on the parabola. Put these values in our formula to find p.
{{{1^2=4p(3)}}}
Thus {{{p=1/12}}}

And our equation becomes
{{{(x-3)^2=(1/3)(y-2.5)}}}
{{{3(x-3)^2+2.5=y}}}

Another way to think about this is that the non-vertex point you are given is only 1 unit over to the right and it goes up 3 units from the vertex, so your "a" value would logically be 3 (1 increase of x results in 3 increase in y).
I edited this because I made it more complicated than it needed to be prior to this current revision. Good day
{{{graph( 300, 300, -2, 6, -2, 6, 3(x-3)^2+2.5)}}}