The height h in feet of a projectile launched upward at a speed of 32 feet/ second from a height of 48 feet is given by the function : h(t) =16^2+32t +48. how long will it take the projectile to hit the ground?

If you are talking about parabolic motion, physics tells us that it goes up to a max and then drops down to the ground.  This type of a parabola is a negative parabola, so I believe your formula should begin with a negative on that 16.  Anyway, when you want to find how long it takes to hit the ground, you are looking for the values of t when the height is 0, since there is no height when an object is laying directly on the ground.  Set the parabola equal to 0 and factor for the values of t.  .  Factor out a -16 to make things a bit easier: .  Of course -16 doesn't equal 0, so factor your quadratic to get the factors of (t-3)(t+1).  There are 2 things in math that will never ever be negative and those are time and distance/length.  Therefore, of our solutions t = 3 and t = -1, we would choose t = 3.  In other words, it takes 3 seconds for the object to hit the ground when it is launched from a height of 48 feet at an initial upwards velocity of 32 feet/second.