Algebra

# Completing the Square

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

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

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

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

What do we get when we complete the square for

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

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