SOLUTION: A ball was kicked into the air from a balcony 20 feet above the ground, and the ball's height above the ground in feet t seconds after the ball was kicked is h(t) = 20 - 16t2 + 32t
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Question 1114527: A ball was kicked into the air from a balcony 20 feet above the ground, and the ball's height above the ground in feet t seconds after the ball was kicked is h(t) = 20 - 16t2 + 32t. What was the maximum height, in feet, of the ball above the ground after it was kicked?
The height of the ball over the ground is described by a quadratic function
h(t) = - 16*t^2 + 32t + 20. (1)
The maximum height is achieved when the quadratic function (1) has the maximum.
From algebra, the quadratic function y = ax^2 + bx + x has extremum at x = .
In your case, a= -16, b= 32, so x= = 1.
Thus the quadratic function (1) achieved maximum at t = 1. It means that the ball will achieve the maximum height at t= 1 seconds.
And the maximum height will be h(1) = -16*1^2 + 32*1 + 20 = 36 ft.
Answer. The ball will achieve its maximum height of 36 ft in 1 second.
