2025 Paradigm Sec 3 Mock EOY Q2

[Complete The Square]

A dolphin jumps out of the water during a dolphin show. The height, \(y\text{ m}\), of the dolphin is given by \(y=-4.5t^2+9t\), where \(t\) is the time in seconds after the dolphin jumps out of the water.

1. Express \(y=-4.5t^2+9t\) in the form \(y=a(t-h)^2+k\).[2]
2. How long did it take the dolphin to reach the maximum height and[2]
   what is the maximum height?[2]
3. Find the range of values of \(t\) where the height of the dolphin is at least \(3.375\text{ m}\).[4]