Suppose that you have a spring gun that you use to launch a small metal ball. You try the first two settings of the gun. The first setting compresses the spring by 1 cm and fires the ball a distance of 0.25 m . The second setting compresses the spring by 2 cm and fires the ball a distance of 1 m .
Assuming that the relationship between spring compression and height is quadratic, how far will the ball go at the highest setting, which compresses the spring 3 cm ?