Solving Quadratic Equations by Factoring - Problem 5

We can use a quadratic formula to relate the input- time an object is in the air, with an output- height of the object. This is often done in physics classes. The equation starts with a gravity constant (-16 for feet per second, and -9.8 for meters per second) multiplied by t squared, plus the initial velocity times t, plus the initial launch height. From there, if we want to find how long it would take until the object reaches the ground, or in this case, reaches the water, we are looking for the x-intercepts of the function (that is, the values of time that make the height zero.) If done correctly, we'll have one positive time that makes sense in the context of this problem, and one negative time that comes from the math model, but doesn't actually make sense in the real world context.