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.
