What is the lower bound for the following equation
This is a quadratic function; therefore $f$ is big-Theta of $n^2$. Therefore, it is both Big-O and Big-Omega of $n^2$. 

However, when a function $f$ is big-Omega of another function $g$, then $f$'s growth is of greater or equal order than $g$. However, since a quadratic grows strictly faster than a linear in the long run, $n^2$ is big-Omega of $n$. Think of as if big-Omega means "greater or equal than".

Also note when $f$ is big-Omega of $g$, then $g$ is big-O of $f$. Obviously, $n$ is big-O of both $n$ and $n^2$.