Aus Online Mathematik Brückenkurs 1

As a starting point, we can take the curve \displaystyle y=x^{2}+2 which is a parabola with a minimum at \displaystyle \left( 0 \right.,\left. 2 \right) and is sketched further down. Compared with that curve, \displaystyle y=\left( x-1 \right)^{2}+2 is the same curve in which we must consistently choose \displaystyle x to be one unit greater in order to get the same \displaystyle y -value. The curve \displaystyle y=\left( x-1 \right)^{2}+2 is thus shifted one unit to the right compared with \displaystyle y=x^{2}+2.