8. The vertex of the parabola is $O$, the focus is $F$, and $M$ is a moving point on the parabola, then the maximum value of $\frac{M O}{M F}$ is $\qquad$
8. $\frac{2 \sqrt{3}}{3}$.

Let the equation of the parabola be $y^{2}=2 p x$, then the vertex $O(0, 0)$ and the focus $F\left(\frac{\sqrt{p}}{2}, 0\right)$. Let $M(x, y)$, then
$$
\begin{array}{l}
\left(\frac{M O}{M F}\right)^{2}=\frac{x^{2}+y^{2}}{\left(x-\frac{p}{2}\right)^{2}+y^{2}}=\frac{x^{2}+2 p x}{x^{2}+p x+\frac{p^{2}}{4}} \\
=\frac{x^{2}+2 p x}{\frac{3}{4} x^{2}+p x+\frac{1}{4}\left(x^{2}+p^{2}\right)} \\
\leqslant \frac{x^{2}+2 p x}{\frac{3}{4} x^{2}+p x+\frac{2 p x}{4}}=\frac{4}{3} . \\
\text { Therefore, } \frac{M O}{M F} \leqslant \frac{2 \sqrt{3}}{3} .
\end{array}
$$

The equality holds if and only if $M(x, y)=(p, \sqrt{2} p)$ or $(p, -\sqrt{2} p)$.