h(t)=-16t^2+200t+25

Question

When does the object reach the maximum height

Answer 1

An object that follows a path that is a quadratic like this will follow the path of a parabola. The maximum height is at the vertex of the parabola. You can find the vertex using the equation x = -b/2a (for f(x) = ax² + bx + c). In this case, "x" is really "t" and a = -16 and b = 200 therefore t_vertex = -200/(2(-16)) = -200/-32 = 6.25

You don't have the units listed in the problem, but it is most likely seconds so the object reaches its maximum height after 6.25 seconds