(Originais Teachy 2023) - Question Very Hard of Mathematics

A ball is thrown vertically upwards from the ground with an initial velocity of 20 m/s. The height h (in meters) that the ball reaches after t seconds is given by the function h(t) = -5t^2 + 20t. Considering that the acceleration due to gravity is 10 m/s^2, and knowing that the quadratic function h(t) describes the ball's motion at time t, answer: (1) What is the maximum height the ball reaches? (2) How long does it take for the ball to reach this maximum height? Justify your answers, demonstrating the calculation clearly and in detail. Additionally, discuss how the quadratic function h(t) relates to uniformly varied motion (MUV), specifically with the concept of vertical launch, including the influence of the quadratic term in describing the motion.