Question

A golfer hits the golf ball. The quadratic function y = -16^2 + 80x gives the time xseconds when the golf ball is at height y feet. How high does the golf ball get before it begins to return to the ground?

A. 80 ft
B. 16 ft
C. 50 ft
D. 100 ft

Answer 1

To determine the maximum height reached by the golf ball before it returns to the ground, we can analyze the given quadratic function:

y = -16x^2 + 80x

This quadratic function represents the height of the golf ball at time 'x' seconds. The maximum height occurs at the vertex of the quadratic equation, which can be found using the formula: x = -b / (2a).

For this function, a = -16 and b = 80. Substituting these values into the formula, we have:

x = -80 / (2 * -16)

x = -80 / -32

x = 2.5

To find the maximum height, substitute this value of 'x' back into the original equation:

y = -16(2.5)^2 + 80(2.5)

y = -16(6.25) + 200

y = -100 + 200

y = 100

Therefore, the golf ball reaches a height of 100 feet before it begins to return to the ground.

The correct answer is D. 100 ft.

Explanation: