Question 127806
The equation of a parabola with vertex at (h,k), and directrix at {{{y=k-p}}} is {{{(x-h)^2=4p(y-k)}}}.


The vertex is given, so we can write:


{{{(x-6)^2=4p(y+4)}}}


Now we have to calculate p given that the parabola passes through (1,8).


{{{(1-6)^2=4p(8+4)}}}


{{{25=48p}}}


{{{p=25/48}}}


Now we have:
{{{(x-6)^2=4(25/48)(y+4)}}}


{{{x^2-12x+36=(25/12)(y+4)}}}


{{{(12/25)(x^2-12x+36)=y+4}}}


{{{(12x^2-144x+432-100)/25=y}}}


So:  {{{f(x)=y=(12x^2-144x+332)/25}}}


{{{drawing(600,600,-10,10,-10,10,grid(1),
graph(600,600,-10,10,-10,10,(12x^2-144x+332)/25)

)}}}