Question

The graph below models the path of a golf ball after it was hit. Write an equation in vertex form that represents the path of the ball.

Answer 1

For the parabola of this form (intersecting the x-axis at two points and opening downwards), the general form would be:

(x - h)² = -4a(y - k)
where
the vertex has coordinates (h,k)

From the figure, the vertex is at (50,150). Using one point which is at (0,0), we can determine a and complete the form:

(0 - 50)² = 4a(0 - 150)
-4a = 50/3

Thus, the complete formula is
(x - 50)² = -50/3(y - 150)