Question 443938
First we need to find the standard form of the parabola equation:

{{{3y=x^2-6x+18}}} => {{{x^2-6x+9=3y-9}}} => {{{(x-3)^2=3(y-3)}}}.

The final equation is the equation of parabola with vertex (3, 3).

Since 4c=3 we get c=3/4, and the focus is (3, 3+3/4) or (3, 15/4).

The directrix is y=3-3/4=9/4.

{{{graph(600, 600, -10, 10, -10, 10, (1/3)x^2-2x+6)}}}