I need help with this college algebra

Question

A projectile is launched from ground level with an initial velocity of v 0 feet per second. Neglecting air​ resistance, its height in feet t seconds after launch is given by s equals negative 16 t squared plus v 0 t. Find the​ time(s) that the projectile will​ (a) reach a height of 208 ft and​ (b) return to the ground when v 0 is 96 feet per second.

Answer 1

The maximum height will occur when the derivative = 0, i.e. -32t + 96 = 0 and the projectile will hit the ground when -16t² + 96t = 0. You solve it from here.

Oh, if you don't have calculus yet, the maximum height will occur at the vertex of the parabola, i.e. at t=96/32.