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Problem of the Week
Problem E
Parabolic Art

Kenna likes making artistic creations using parabolas, to put on the walls of her math classroom. She drew a parabola with vertex \(E(7,9)\) and plotted points \(A(9,8)\) and \(B(3,b)\) on the parabola as well as points \(C\) and \(D\) where the parabola intersects the \(x\)-axis, with \(C\) to the left of \(D\). Then she connected points \(A\), \(B\), \(C\), and \(D\) to form quadrilateral \(ABCD\), and painted it blue. What is the area of quadrilateral \(ABCD\)?

A region in the first quadrant of the Cartesian plane is bounded above by a downward opening parabola and below by line segment CD along the x-axis. Points B, E and A are plotted on the parabola from left to right. Quadrilateral ABCD is contained within the region.