Calculate the range of $f$. Calculate the range of the function $f$ with $f(x) = x^2 - 2x$, $x\in\Bbb{R}$. My book has solved solutions but I don't get what is done:
$$f(x) = x^2 - 2x + (1^2) - (1^2)= (x-1)^2 -1$$
edit: sorry for wasting all of the people who've answered time, I didnt realize that I had to complete the square....  Wish I could delete it but I cant

Hint:
i suppose that you are convinced that $f(x)=x^2-2x=(x-1)^2-1$. Now write this as: $f(x)=-1+(x-1)^2$ and note that the square is always not negative, and it is null for $x=1$.
So what you can say about $f(x)$?
