Question

When Alex hit a golf ball, it traveled a horizontal distance of 200 feet, and at its highest reached 72 feet. Write and equation to model the path of the golf ball.

Answer 1

Let x be the horizontal distance (ft) from where Alex hit the ball and y the height (ft). The parabola has vertex at (100,72) and passes through (0,0), so use vertex form:

y = a(x − 100)^2 + 72.

Solve for a using (0,0): 0 = a(−100)^2 + 72 ⇒ a = −72/10000 = −0.0072.

Thus an equation is

y = −0.0072(x − 100)^2 + 72,

which expands to

y = −0.0072x^2 + 1.44x.