Problema Solution
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 wasw kicked was
h(t) = 20 −16t2 + 32t. What was the maximum height, in
feet, of the ball above the ground after it was kicked?
Answer provided by our tutors
we need to find the maximum of the parabolic function:
h(t) = 20 −16t^2 + 32t
H9t) = -16t^2 + 32t + 20
since the quotient in front of t^2 is -16 < 0 the function has maximum in its vertex:
h max = c - b^2/(4a) where a = -16, b = 32, c = 20
h max = 20 - 32^2/(4*(-16))
by solving we find
h max = 36 ft
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the maximum height of the ball after it was kicked was 36 feet.