An object is thrown upward from the top of a 112​-foot building with an initial velocity of 96 feet per second. the height h of the object after t seconds is given by the quadratic equation h= -16t^2 + 96t + 112. when will the object hit the​ ground?

When you factor this quadratic (or any polynomial, for that matter), what you get are the zeros of the function.  When the object is on the ground, its height is 0.  The zeros of a function are where the graph goes through the x-axis.  Where the graph goes through the x-axis, the y value is 0.  Using the quadratic formula to factor this gives you zeros of t = -1 and t = 7.  The two things in math that will never EVER be negative are time and distance/length, so we know that object will hit the ground 7 seconds after it is thrown.