The Archer and the Discriminant

This GeoGebra worksheet demonstrates a visual application of the discriminant.  When friction is neglected, the path of an arrow can be modeled using a quadratic function.  GeoGebra randomly generates an initial velocity (the vertical component), an initial height, and a target height.  Then it calculates the discriminant of the resulting quadratic equation and asks whether or not the arrow will reach the desired height.  The arrow is then fired so that we can see if our prediction is correct.