Question

Lorraine hits a golf ball into the air. It lands 60 feet away from her. At its highest point, the ball is 30 feet in the air. Find the parabolic equation that describes the height of the ball as it moves away from Lorraine. Use this equation to evaluate the function to answer the following question: What is the height of the golf ball when it is 15 feet away from Lorraine? (I point)
___feet

Answer 1

Let x be the horizontal distance (feet) from Lorraine and y the height (feet). The parabola has zeros at x = 0 and x = 60 and vertex at x = 30, y = 30. In vertex form:

y = a(x − 30)^2 + 30.

Using (0,0): 0 = a(−30)^2 + 30 → 900a = −30 → a = −1/30. So

y = −(1/30)(x − 30)^2 + 30,

which expands to y = −(1/30)x^2 + 2x.

At x = 15: y(15) = −(1/30)(15)^2 + 2(15) = −225/30 + 30 = −7.5 + 30 = 22.5.

Answer: 22.5 feet.