Answer
The interval is $[0, 3]$
$0\leq t \leq 3$
Work Step by Step
To find the interval, we can simply calculate when the ball will be at $h=32$ and all the values greater than the point will be $32ft$ or more above the ground.
$h<128+16t-16t^2$
$-16t^2+16t+128=32$
$-16t^2+16t+96=0$
$-t^2+t+6=0$
$t^2-t-6=0$
$t_1=-2$ ; $t_2=3$
(time cannot be negative)
$t=3$
So, the interval during which the ball will be at least $32ft$ above the ground is $[0, 3]$
$0\leq t \leq 3$
