We need the maximum value of a quadratic function.

The maximum value of a quadratic function 

f(x) = ax^2 + bx + c

with a negative leading coefficient, is when the value of x
equals 

In this problem x is t and f is h, a is -16 and b is +32
c is 4 but we don't need it to find the time t when the
function h(x) (for height) has its maximum value.

h(t)=-16t^2+32t+4



So it reaches the maximum height in 1 second.  So we
substitute 1 for t in the equation

h(1) = -16(1)^2+32(1)+4 = -16+32+4 = 20 feet.

So yes, that's high enough for him to catch the orange.

Edwin