jmc

Write $x^2-6x$ as $(x-3{)}^2-9$ to obtain $$y=(x-3{)}^2+4.$$Since $(x-3{)}^2\ge 0$, we have $y\ge \boxed{4}$. The value $y=4$ is obtained when $x=3$. (Note: this method of rewriting a quadratic expression is called ``completing the square'').