Completing the Square
This applet demonstrates a geometric interpretation of the method of completing the square. The construction was first described during the 9th century by the great Persian mathematician Al-Khwarizmi in his book The Compendious Book on Calculation by Completion and Balancing.
We consider the equation .
A quadratic function can be written as ax2+bx+c.
1. Enter a value of b (coefficient of x)
2. Keep slowly sliding. Next, we divide the rectangle into two parts and move them, preparing to form a square.
3. Keep slowly sliding. We are COMPLETING THE SQUARE (geometrically, instead of algebraically.) The orange square completes our large square.
Describe the pattern you noticed.
What number needs to be added to the following parts to make them a perfect square?
Write the general rule for x2+bx.