Aus Online Mathematik Brückenkurs 1

By completing the square, we can rewrite the function as

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

and when the function is written in this way, we see that the graph \displaystyle y = (x-3)^{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 a and b).

The graph of f(x) = x²		The graph of f(x) = x² - 6x + 11