[size=150] This applet demonstrates a geometric interpretation of the method of completing the square. The construction was first described during the 9[sup]th[/sup] century by the great Persian mathematician Al-Khwarizmi in his book [i]The Compendious Book on Calculation by Completion and Balancing[/i].[br]We consider the equation [math]x^2+bx=c[/math].[/size][br]
A quadratic function can be written as [b] ax[sup]2[/sup]+bx+c.[/b][br]1. Enter a value of b (coefficient of x) [br][br]2. Keep slowly sliding. Next, we [b]divide the rectangle[/b] into two parts and move them, preparing to form a square.[br][br]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.
[b]What number [/b]needs to be added to the following parts to make them a perfect square?[img]data:image/png;base64,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[/img]
[table][tr][td][/td][td] Number added [/td][td] Prefect Square [/td][/tr][tr][td]a.[/td][td][/td][td][/td][/tr][tr][td]b.[/td][td][/td][td][/td][/tr][tr][td]c.[/td][td][/td][td][/td][/tr][tr][td]d.[/td][td][/td][td][/td][/tr][tr][td]e.[/td][td][/td][td][/td][/tr][tr][td]f.[/td][td][/td][td][/td][/tr][tr][td]g.[/td][td][/td][td][/td][/tr][/table]
Write the general rule for x[sup]2[/sup]+bx.