Question

how would you find the equation of the graph of a parabola?

Answer 1

the biggest hint will probably be the location of the vertex of the parabola.... once you determine that, there still might be other things needed to determine the equation from the graph.... do you have an example?

Answer 2

If it's concave up:
\[(x-h)^2=4a(y-k)\]
where (h, k) is the vertex and a is the focal length. (the distance between the focus S(0, a) and the origin)
Concave down:
\[(x-h)^2=-4a(y-k)\]