Calculus approach:
Take the derivative of that equation, you get
\[h'(t)=-32t+70\]
Find out where -32t + 70 = 0 , and that's where the maximum point is (cause the slope changes from positive to negative at that point).
Then you can plug t back into h(t) to get the height.
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satellite73:
you can do this without calc. you are looking for the vertex
the first coordinate of the vertex of \(ax^2+bx+c\) is always \(-\frac{b}{2a}\) which in your case is \[-\frac{70}{2\times (-16))}\]
satellite73:
since you are going to use a calculator anyways, round that to \(2.19\) and plug it in, i.e. computer \[-16\times (2.19)^2+70\times (2.19)+2\]
satellite73:
let me know when you get the answer
zarkam21:
85.22
satellite73:
i got \(78.56\)
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