Aus Online Mathematik Brückenkurs 1

By completing the square, we can rewrite the function as

\displaystyle f\left( x \right)=x^{2}-6x+11=\left( x-3 \right)^{2}-3^{2}+11=\left( x-3 \right)^{2}+2,

and when the function is written in this way, we can see that the graph \displaystyle y=\left( x-3 \right)^{2}+2 is the same curve as the parabola \displaystyle y=x^{2}, but shifted two units up and three units to the right (see sub-exercise d and e).