SOLUTION: The quadratic function that models the fireworks� height s(x) in feet x seconds after they are launched is given by the equation s(x) = -16x^2+200x + 4. When should the fireworks

Click here to see ALL problems on Quadratic Equations

Question 87764This question is from textbook Intermediate Algebra
: The quadratic function that models the fireworks� height s(x) in feet x seconds after they are launched is given by the equation s(x) = -16x^2+200x + 4. When should the fireworks explode so that they go off at the greatest height? What is that height? [Hint: Find the vertex of the quadratic function s(x).] This question is from textbook Intermediate Algebra

Found 2 solutions by stanbon, rapaljer:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The quadratic function that models the fireworks� height s(x) in feet x seconds after they are launched is given by the equation s(x) = -16x^2+200x + 4. When should the fireworks explode so that they go off at the greatest height? What is that height? [Hint: Find the vertex of the quadratic function s(x).]
-----------
Vertex occurs at x=-b/2a = -200/-32 = 6.25 seconds
Height at that time = s(6.25) = -16^(6.25)^2+200(6.25)+4 = 668.07 ft
=============
Cheers,
Stan H.

Answer by rapaljer(4671) (Show Source):
You can put this solution on YOUR website!
The vertex of the parabola occurs at .
Therefore, for your function , the vertex occurs at seconds.

The maximum height is at feet. By the way, I used a graphing calculator, with window: x= [-2,14], y = [-100, 700]. It looks like this:

R^2 Retired from SCC