Math Help - Quadratic equation problem..

Fireworks are launched into the air. The quadratic function

s(t)=-4t^2+50t+1

models the fireworks' height, s(t) in metres, t seconds after they are launched.

a) when should the fireworks explode so that they go off at the greatest height?
b) what is that height?

2. Find the midpoint of the parabola with:

$- \frac{b}{2a}$

(That will give you the time at which it should explode.)

And to find the height simply plug that time in for t and it will give you a maximum.

3. set first derivative of the function to zero and solve for t ,,,that gives u the t at max height......t=50/8 ...to find max height ,,calculate s(t) for t =50/8 .