Question 292489
The height h in feet reached by a dolphin t seconds after breaking the surface of the water is given by h = -16t^2 + 32t
How long will it take the dolphin to jump out of the water and touch the trainer's hand? 
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You don't mention how high up the trainer's hand is...  But, I'll assume it is at the highest point at which the dolphin can jump.  If so, you can find this by finding the "axis of symmetry":
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t = -b/2a
t = -32/(2(-16))
t = -32/(-32)
t = 1 second