so hmmm notice the picture below
the ball goes up up reaches the vertex, then goes down down,and when it hits the ground, y = 0
thus [tex]\bf 0=-16t^2+16t+32\implies 0=-16(t^2+t+2)
\\\\\\
0=t^2-t-2[/tex]
and surely, you know how much that is
so, the domain is from 0 to "t" when y = 0, or the ball hits the ground
