SOLUTION: A soccer ball is kicked straight up with an initial velocity of 32 ft. per second. Its height above the earth is given by s (t) = -16t2 + 32t, where,�s� is the height in ft. at any

Question 212103: A soccer ball is kicked straight up with an initial velocity of 32 ft. per second. Its height above the earth is given by s (t) = -16t2 + 32t, where,�s� is the height in ft. at any time, �t� seconds.
What is the maximum height reached by the ball?
How long after it was thrown up the ball reaches its maximum height?

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A soccer ball is kicked straight up with an initial velocity of 32 ft. per second. Its height above the earth is given by s (t) = -16t2 + 32t, where,�s� is the height in ft. at any time, �t� seconds.
What is the maximum height reached by the ball?
How long after it was thrown up the ball reaches its maximum height?
.
The "vertex" of the parabola will give you both.
.
First, find the "axis of symmetry":
t = -b/2a
t = -32/2(-16)
t = -32/-32
t = 1 second (answer to second question)
.
The "height" is found by plugging the value above back into:
s(t) = -16t^2 + 32t
s(1) = -16(1)^2 + 32(1)
s(1) = -16 + 32
s(1) = 16 feet (answer to first question)

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