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A ball is thrown straight upward with a velocity of 90 ft/sec.
Its height above the ground after t seconds is h = 90t - 16t2.
What is the maximum height that the ball reaches?
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This quadratic function can be factored into the product
h = 90t - 16t^2 = t*(90-16t).
From this decomposition, the zeroes of this quadratic function (its x-intercepts) are
t = 0 second and t = = 5.625 seconds.
This quadratic function achieves its maximum value half-way between x-intercepts.
So, = = 2.8125 seconds.
To find the maximum height, simply substitute this value t = = 2.8125 into the formula and get
= 90*2.8125 - 16*2.8125^2 = 126.5625 ft = 126.6 ft (rounded as requested).
Solved.