the equation for a firework is h=-5d2+20d+1
h=height above the ground
What would the max height of the firework be?
You are attempting to maximize
differentiating we get
So now we need to find where this equals zero
to verify this is a max we use the second derivative test
we can see that this is in fact a max
Judging from the questions you posted, this is probably what you want done:
Complete the square to get your equation in the form of:
where the sign of a determines which way the parabola points up (should be negative if you're looking for a max) and (b, c) is your vertex.
The vertex should be the highest point of the parabola and that'll be your answer.