Answer:
y = (-1/2)(x-5)^2 - 4.5
Step-by-step explanation:
The general formula for a vertical parabola is 4py=x^2.
Here the vertex is not at (0,0), but rather is at (5, -4.5) (halfway between the focus and the directrix). The graph of the parabola opens down, because the directrix is higher up the y-axis than the focus.
Thus, this equation becomes 4p(x+4.5) = (x-5)^2.
Here p = half the distance between the focus and the directrix, or 0.5. Because the graph opens downward, use p = -0.5.
Then we have 4(-0.5)(y+4.5) = (x-5)^2, or
-2 (y + 4.5) = (x-5)^2, or
y + 4.5 = (-1/2)(x-5)^2, or
y = (-1/2)(x-5)^2 - 4.5
