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

For any $y\in\Bbb{R}$, $y^2\ge0$. So $y^2-1\ge-1$.
Substitute $y=x-1$. What does it imply? 
