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Completing The Square

Learn how to eliminate the linear term and see through messy quadratics. You’ll know just how high to shoot your three-pointer to avoid tall defenders.

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



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