2023 AISS AM S3 EOY Q4

A golfer hits a ball such that the height, \({h}\) metres, of the ball above the ground \({t}\) seconds later is given by

\({h = 0.2t(40 - t)}\).

1. By expressing the function in the form \({h = a(t - m)^2 + n}\), where \({a}\), \({m}\) and \({n}\) are constants, explain whether the ball can reach a height of \({100}\) metres.[2]
2. Find the range of values of \({t}\) for which the ball is at most \({75}\) metres above the ground.[4]