In a word problem about ballistics, what does the absolute maximum of a quadratic function represent?
The absolute maximum represents two things:
- Where the ballistic is at rest vertically
- 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.