
Arturo O. answered 08/25/18
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If up is positive and down is negative, the correct equation is
s(t) = -16t2 + 128t + 4
[The minus sign is missing in the first term of the given equation.]
Maximum height occurs at the vertex of the height-vs.-time parabola, which is at
t = -128/[2(-16)] sec = ? sec
Now plug the result for t into s(t) to get maximum height. You should be able to finish from here.