Question 54311
You can do either.  The quadratic formula was derived by completing the square, I could bore you by proving that, but you only have an hour, besides that only helps you to find the time it takes for it to hit the ground!  What you need is the vertex of this parabola (that's the maximum height).  You can find this two ways:
h(t)=-16t^2+96t+5 is in ax^2+bx+c form.
The value for t in the vertex is found by the formula {{{highlight(t=-b/(2a))}}}.
Take that value and plug it back in for t in your t function.  This will be the max height of the ball.
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The second way is to put this in vertex form, you do this by completing the square.
{{{highlight(h(t)=a(t-h)^2+k))}}} (h,k) is the vertex and k is the Maximium height.
Good Luck!
Happy Calculating!!!