(Originais Teachy 2023) - Question Medium of Mathematics

A ball is kicked upwards from the ground with a force that makes it describe a trajectory that can be modeled by a quadratic function. This function represents the height h(t) of the ball in meters, t seconds after the kick, and is given by h(t) = -5t² + 20t. Considering the physical context of the situation, where h(t) is the height of the ball and t is the time elapsed since the kick, answer: 1) What is the maximum height the ball reaches and when does this occur? 2) What is the initial velocity of the ball at the moment of the kick? Justify your answers using the concepts of the vertex of the parabola and the derivative of the function h(t).