Question

Ferdinand is playing golf. He hits a shot off the tee box that

has a height modeled by the function h(t) = –16t2 + 80t,
where h(t) is the height of the ball, in feet, and t is the time
in seconds it has been in the air. The graph that models
the golf ball's height over time is shown below.

When does the ball reach its maximum height?

What is the maximum height of the ball?

Answer 1

Maximum height of the ball = 100 m

Time to reach the maximum height = 2.5 seconds

Explanation:

Function that models the height h(t) of the ball and time 't',

h(t) = -16t² + 80t

Convert this equation into vertex form,

h(t) = -16(t²- 5t)

= -16[t² - 2(2.5t) + (2.5)² - (2.5)²]

= -16[[t² - 2(2.5t) + (2.5)²] + 16(2.5)²

= -16(t - 2.5)² + 16(6.25)

= -16(t - 2.5)² + 100

By comparing this equation with,

g(t) = a(x - h)² + k

Here, (h, k) is the vertex of the parabola.

Vertex of the given parabola will be → (2.5, 100)

Therefore, maximum height of the ball = 100 m

Time taken by the ball to reach the maximum height = 2.5 seconds