Entire functions with $|f(z)|\le M|z|^2$ are quadratic polynomials

Let $f(z)$ be entire and assume that $f(z) \le M\abs{z}^2$ outside some disk for some constant $M$. Show that $f(z)$ is a polynomial in $z$ of degree $\le 2$.

Erratum: the source writes the hypothesis as $f(z) \le M\abs{z}^2$, which has no meaning for complex values of $f$. The intended hypothesis is $\abs{f(z)} \le M\abs{z}^2$ outside some disk.