2025 CGSS PRELIMS P2 Q1

An object was launched from a machine. Its height, \(y\) metres above ground, \(t\) seconds after launch, can be modelled by a quadratic function \(y=f(t)\). Four seconds after launch, the object reached its maximum height of 81 m and then dropped to a height of 54 m after a further three seconds.

1. Find the initial height of the object when it was launched.[4]
2. Without solving a quadratic equation, explain and determine how long did the object stay above 54 m?[2]