Question

A ball is projected up into the air from the surface of a platform to the ground below. The height of the ball above the ground, in feet, is modeled by the function f(t)= -16t^2 + 96t + 112, where t is the time, in seconds, after the ball is projected. State the height of the platform, in feet. State the entire interval over which the ball's height is decreasing.​

Answer 1

• 112 ft
• 3 - 7 seconds interval

Explanation:

Given function:

• f(t) = -16t² + 96t + 112

The height of the platform is the y-intercept, when t = 0:

• f(0) = - 16*0 + 96*0 + 112 = 112 ft

The ball's height is decreasing once it reaches the maximum, which is at vertex.

The vertex is at x = -b/2a:

• t = - 96/ - 32 = 3

The ball hits the ground when f(t) = 0:

• - 16t² + 96t + 112 = 0
• t² - 6t - 7 = 0
• (t - 7)(t + 1) = 0
• t = 7 (positive root)

The interval is between 3 seconds and 7 seconds