Question

In a word problem about ballistics, what does the absolute maximum of a quadratic function represent?

Answer 1

The absolute maximum represents two things:

1. Where the ballistic is at rest vertically

and

1. The halfway point of the arc

The first is moderately easy to see: heading up to the max, the ball is moving upward and afterward it is moving downward.

The second is a property of a parabolas. The midpoint is halfway between any two points at the same height. Therefore, if you're shooting a ballistic on flat ground, the distance it will go is twice the distance to the peak.