Aball is thrown downward from the top of a 140-foot building with an initial velocity of 16 feet per second. the height of the ball h in feet after t seconds is given by the equation h equals negative 16 t squared minus 16 t plus 140. how long after the ball is thrown will it strike the ground?

When the ball hits the ground, it has a height of 0.  When you factor a polynomial, what you get as your solutions are the zeros of the function.  Those zeros are where the graph goes through the x-axis.  When the graph goes through a point ON the x-axis, y is equal to 0.  Therefore, by factoring and finding the zeros, we can determine when the ball hits the ground.  Use the quadratic formula to find that the zeros, or solutions, or roots, are t = -3.5 seconds and 2.5 seconds.  The two things in math that will never EVER be negative are time and distance/length.  Therefore, the ball hits the ground 2.5 seconds after it was thrown.