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