Answer
The vertex is at $(2.8,125.44)$.
Work Step by Step
$h=-16t^2+89.6t\\h=-16(t^2-5.6t)\\h=-16((t-2.8)^2-2.8^2)\\h=-16(t-2.8)^2+16\cdot2.8^2\\h=-16(t-2.8)^2+125.44$
The vertex is at $(2.8,125.44)$ which means that the maximum height of the water is $125.44$ ft, and this happens after $2.8$ seconds.
