Completing the square for Quadratic Expressions

[size=150][b]Objective of Activity : Understanding "Completing the Square" technique[br][/b][br]The technique of "completing the square" where the quadratic expression [math]x^2+bx[/math]is transformed into [math]\left(x+\frac{b}{2}\right)^2-\left(\frac{b}{2}\right)^2[/math] or [math]\left(x+h\right)^2+k[/math] where [math]h=\frac{b}{2}[/math] and [math]k=-\left(\frac{b}{2}\right)^2[/math][br]can be visualised in this tutorial lesson.[br][br][/size][size=150]Explore and attempt to answer the question in the interactive activity below. [br]Click on the "New Expression" button to generate a few more questions and do them. [br][br]Then answer the questions below this activity.[/size]
[size=200][b]Check Your Understanding[br][/b][/size][br][size=150]Try answering the questions below to see if you have understood "Completing the Square"[br][br][/size][b][i](Do attempt the questions on a piece of paper before selecting what you think is the most appropriate answer.)[/i][/b]
[size=150]1. Express [math]x^2+bx[/math][/size] in the form of [math]\left(x+h\right)^2+k[/math] where [math]h[/math], [math]k[/math] are in terms of [math]b[/math]
[size=150]2. Express [math]x^2+6x[/math][/size] in the form of [math]\left(x+h\right)^2+k[/math]
[size=150]3. Express [math]x^2-bx[/math][/size] in the form of [math]\left(x+h\right)^2+k[/math] where [math]h[/math], [math]k[/math] are in terms of [math]b[/math]
[size=150]4. Express [math]x^2-10x[/math][/size] in the form of [math]\left(x+h\right)^2+k[/math] where [math]h[/math], [math]k[/math] are in terms of [math]b[/math]
[size=150]5. Express [math]x^2+bx+c[/math] in the form of [math]\left(x+h\right)^2+k[/math][/size]
[size=150]6. Express [math]x^2+4x+1[/math] in the form of [math]\left(x+h\right)^2+k[/math][/size]
[size=150]7. Express [math]x^2-bx+c[/math] in the form of [math]\left(x+h\right)^2+k[/math][/size]
[size=150]7. Express [math]x^2-2x+5[/math] in the form of [math]\left(x+h\right)^2+k[/math][/size]
[size=150]7. Express [math]x^2-8x-2[/math] in the form of [math]\left(x+h\right)^2+k[/math][/size]
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Information: Completing the square for Quadratic Expressions