An object is thrown upward from the top of a 144-foot building with an initial velocity of 128 feet per second. the height h of the object after t seconds is given by the quadratic equation h= -16t^2 + 128t + 144. when will the object hit the ground?

9 seconds

You want to find t for h = 0. Using your equation, this is ...

... 0 = -16t² +128t +144

... 0 = t² -8t -9 . . . .  divide by -16

... (t +1)(t -9) = 0 . . . factor

... t = -1 or +9 . . . . . . for this problem, the -1 solution is extraneous.

The object will take 9 seconds to hit the ground.

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