Maximum area under a parabola

Overview

P moves on a parabola; maximize area of △PAB (vertical height).

Explanation

If chord AB lies on the x-axis and P is on the parabola, S = ½·AB·|y_P|.
Area tracks |y_P|; for a downward-opening parabola the vertex maximizes |y| and area.
In general write area as a function of a parameter, then optimize.

How to use

Drag P along the curve and find where vertical height (and area) peak.

Knowledge points

• Quadratic functions
• Moving points