the directrix is above the vertex. That means it's a downward opening parabola with general form of
y=a(x+h)^2 + k, where the vertex is (h,k) and a<0
y=a(x-0)^2 +5
y=ax^2 +5. The directrix is 3 units above the vertex. the focus is 3 units below the vertex. Focus is (0,2). A parabola is the collection of all points that are equally distant from the focus and the directrix. Find another point on the parabola, directly to the right of the focus. It will be (x,2) and will be 6 units to the right of the focus, the same distance as to the directrix. It will be (6,2) Plug that point into the general equation to calculate a, the coefficient of the x^2 term. Axis of symmetry is x=0. Another point on the parabola is (-6,2)
2 =a((6)^2 +5
-3 = 36a
a =-3/36 =-1/12
y=(-1/12)x^2 + 5 which is the standard form
or
y=-x^2/12 + 5 or
12y =-x^2 + 60 is the parabola with directrix y=8 and vertex = (0,5)
