SOLUTION: I was wondering if someone could help me with this one. Thank you. For fireworks that are launched into the air, the formula h = -16t^2 + 200t + 4 models the fire

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Question 16327: I was wondering if someone could help me with this one.
Thank you.
For fireworks that are launched into the air, the formula

h = -16t^2 + 200t + 4

models the fireworks' height h, in feet, t seconds after they are launched.
When should the fireworks explode so that they go off at the greatest height?
What is that height?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The equation: h+=+-16t%5E2+%2B+200t+%2B+4 describes a parabola. You need to find the location of the vertex of this parabola which will be a maximum since the parabola opens downwards (-16t^2). The horizontal coordinate (t-component) of the vertex is given by: -b%2F2a. This corresponds to the time, t, at which the firework will reach its maximum height.
So, the maximum height will occur at: -200%2F2%28-16%29 = 25%2F4secs = 6.25 seconds. This is when the firework should be detonated for it to explode at the greatest height.
To find this maximum height, substitute t = 6.25 into the original equation and solve for the height, h. It's easier to use the fractional form, 25/4
h+=+-16%2825%2F4%29%5E2+%2B+200%2825%2F4%29+%2B+4
h+=+-16%28625%2F16%29+%2B+50%2825%29+%2B+4
h+=+-625+%2B+1250+%2B+4
h+=+629feet.