Posted by Kiley on Sunday, February 10, 2013 at 9:16pm.
If you know Calculus,
h ' (t) = -32t + 80
= 0 for a max height
t = 80/32 = 5/2 or 2.5 seconds
h(2.5)= -16(2.5)^2 + 80(2.5) + 12
= 112 ft
If you don't know calculus, let's complete the square
h(t) = -16(t^2 - 5t + 25/4 -25/4 + 12
= -16( (t-5/2)^2 - 25/4) + 12
= -16(t-5/2)^2 + 100 + 12
= -16(t-5/2)^2 + 112
the vertex is (5/2 , 112)
so the max of h is 112 , when x = 5/2 as above
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