If you write the eqation of a parabola as , the same as your formula with [itex]h= x_0[/itex], [itex]k= y_0[/tex], where [itex](x_0, y_0)[/itex] is the vertex, then the focal length is f= 1/4a.Parabola - Wikipedia, the free encyclopedia

Saying that the vertex is at (0, 3) and the focus is at (0, 0) means that the focal length is f=1/4a= 3 so that 4a= 1/3, a= 1/12. Of course, because the focus isbelowthe vertex, the parabola opensdownward, so a is negative.