What is the lower bound for the following equation f(n) = 32n^2 + 17n + 1.

The lecture slide says that lower bound can be Omega(n^2) or Omega(n).

Some body please guide me why the lower bound can be Omega (n). i know the upper bound which is O(n^2).

Zulfi.
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 $n^2$.