h(t)=-16t^2+96t+112

The arrow reaches maximum height when the slope of the curve equals zero.

The slope can be found by taking the first derivative:

h’(t)=-32t+96

h’(t)= 0 when t = 3

h(3)=-16(3^2)+96(3)+112 = -144 + 288 + 112 = 256

So 256 feet is the maximum height.