Hi Haylee,
I hope you know what the directrix is and what is the focus of a parabola.
Let us quickly refresh the vocabulary
Directrix is the line outside the parabola and Focus is a point inside the parabola, vertex is the point on the parabola and it can be minimum or maximum depending on whether the parabola is opening up or down.
vertex is equidistant from the focus and the directrix and that distance we write as ‘p’.
given y=9 is the directrix and vertex is (0,0)
So distance from vertex to directrix is 9 units. Since the directrix y=9 is above the vertex the parabola has to be opening downward and the focus would be at (0,-9)
since parabola opens downwards we will use p=-9
equation of parabola:
(x-h)^2= 4p(y-k) where (h,k) is the vertex
substitute the values h=0, k=0, p=-9 above and you should be able to get the equation
Make sure to divide in the end by the coefficient of y so that you get equation of the form
y=( some constant) x^2
you should probably get y=-1/36 x^2
hope this helps!
