Aball is propelled upwards from ground level. after t seconds it's height in feet is a function defined by f(t)=-16t sq +96t. after how many seconds will it reach a height of 128ft.

Well, we know the height is f(t), and we know that f(t) = -16t² + 96t, with "t" being the seconds.

so, when will it reach 128ft?  namely, what is "t" when f(t) = 128?



well, so it reaches it twice, check the picture below.

at 2 seconds on its way up, and at 4 seconds on its way down.