parabola with vertex (0,8) and focus (0,9)

Question

write the equation in vertex form for the parabola with vertex (0,8) and focus (0,9)

 

Answer 1

The vertex is (h,k) and the focus is (h,k+p) and the equation is (x-h)² = 4p(y-k).

Make the substitutions and you get y = (1/4)(x² + 32).

 

How do I know that?  Look up the equations of a parabola in an analytic geometry textbook!