Algebra

Completing The Square

Completing the Square

         

The quadratic expression x218x+112x^2-18x+112 can be rewritten as (xa)2+b(x-a)^2+b. What is the value of a+b?a+b?

If 3x26x+15=a(xb)2+c,3x^2-6x+15=a(x-b)^2+c, what is the value of a+b+ca+b+c?

As xx ranges over all non-negative real numbers, what is the smallest possible value of x12x+108?x-12\sqrt{x}+108?

If 13x2+6x+10=1a(x+b)2c,\frac{1}{3}x^2+6x+10=\frac{1}{a}(x+b)^2-c, what is the value of a+b+ca+b+c?

What do we get when we complete the square for

12x2+5x+2?-\frac{1}{2}x^2+5x+2?

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