When does it reach maximum height?

H (t) = -16t^2+112t+288

484 feet maximum

Step-by-step explanation:

H (t) = -16t^2+112t+288

The maximum height occurs at the vertex of this graph.

Let us find the vertex.

vertex x-coordinate = - b/2a

x = - b/2a = - (112) / (2*-16) = 7/2 sec.

H (7/2) = - 16 * (7/2) ^2 + 112 * (7/2) + 288

H (7/2) = - 196 + 392 + 288 = 484 feet ...