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ASU 308 All Soviet Union MO min area of rectangle inside y\le-x^2,y\ge x^2-2x+a

Source:

July 23, 2019
geometryrectangleareasminimumparabola

Problem Statement

Given real aa. Find the least possible area of the rectangle with the sides parallel to the coordinate axes and containing the figure determined by the system of inequalities y≤−x2   and   y≥x2−2x+ay \le -x^2 \,\,\, and \,\,\, y \ge x^2 - 2x + a
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