Parabolic Segment

Below is a dynamic Geogebra worksheet showing a parabolic segment determined by the chord AB and the parabola f(x)=a*x^2. The "vertex" of the segment is point C. Also shown is the triangle ABC, and the rectangle ABDE where the side DE is tangent to the parabola at C. The value for the area of each of the three regions is displayed.

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