the equation for a firework is h=-5d2+20d+1
h=height above the ground
d=horizontal distance
What would the max height of the firework be?
I am going to assume two things..firstly d2=dē and secondly, that you are in calc
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
and since
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.