Todd hit a golf ball 180 yards. The maximum height the golf ball reached was 30 yards. Assume the path of the ball is parabolic. Write an equation for the path of the ball.

Question

Todd hit a golf ball 180 yards. The maximum height the golf ball reached was 30 yards. Assume the path of the ball is parabolic. Write an equation for the path of the ball.

Answer 1

it's probably easier to work with feet, instead of yards

max height = 30 yds = 90 ft

h=0 when the ball goes 180 yds = 540 ft

vertex = (270,90)

h(x) = a(x-270)^2 +90 is the parabolic curve in vertex form

to find a, plug in the poing (0,0) or (540,0)

0 = a(0-270)^2 +90

a(270)^2 =-90

a = -90/270^2

a = -1/810

h(x) = (-1/810)(x-270)^2 +90

where x and h are measured in feet, not yards

it might help to draw a rough sketch of the downward opening parabola

plot the vertex and x intercepts, axis of symmetry is: x=270

or try it with yards, if you prefer