An equation for the height as a function of time is

h(t) = -16t^2 + 128t.

To answer the question, you should solve an inequality


h(t) > 128,   or   -16t^2 + 128t > 128.


It is equivalent to 16t^2 - 128t + 128 < 0,  or  t^2 -8t + 8 < 0.


To solve it, solve the quadratic equation t^2 -8t + 8 = 0.


 =  =  = .


Now the answer is:  at  < t <  seconds the projectile's height exceeds 128 feet.