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…
Use the slider to adjust the width of the blue rectangle.
Click Divide Rectangle in Half to bisect the blue rectangle. Then click Move Pieces and Align to place the pieces in a better arrangement around the yellow square.
Click Complete the Square to add the necessary piece to make the arrangement into a complete square.
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).
If you would like to rate this lesson, then please register. Riuscipisci bla feummod
olenim dignit irit luptatum zzriliquamet la commodigna facilit prat.