The act of "completing the square" involves taking half the coefficient of x in the quadratic x2 + ax and adding its square. But many students do not understand why this process works. This interactive geometric proof shows…
The side length of the yellow square is x, and the width of the blue rectangle is a. (You can adjust the width of the rectangle using the slider at the top of the screen.)
The process of "completing the square" involves taking half the coefficient of x. Click the Divide Rectangle in Half button.
Click the Move Pieces and the Align buttons to move the rectangles to a better arrangement. This new arrangement is almost, but not quite, a complete square.
After the square has been completed, adjust the slider for the Rectangle Width (a).
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