KöMaL 2010 C1043

Determine the range of the function given by the following rule of assignment: $f(x)=\frac{{(x+a)}^2}{(a-b)(a-c)} + \frac{{(x+b)}^2}{(b-a)(b-c)} + \frac{{(x+c)}^2}{(c-a)(c-b)}$, where $a$, $b$ and $c$ are different real numbers.