Example 7. If $M=3 x^{2}-8 x y+9 y^{2}-4 x+6 y+13$, then the following statement must be true is ( ).
(A) $M \geqslant 0$
(B) $M0$
(D) $M \leqslant 0$
(1990, Shanxi Province Junior High School Mathematics Competition Preliminary)
$$
\begin{array}{l}
\text { Sol } \because M=3 x^{2}-(8 y+4) x+9 y^{2}+6 y+13, \\
\therefore \quad \Delta_{x}=(8 y+4)^{2}-4 \times 3\left(9 y^{2}+6 y+13\right) \\
=-4\left(11 y^{2}+2 y+35\right). \\
\end{array}
$$

Let $N=11 y^{2}+2 y+35$, then
$$
\Delta_{y}=2^{2}-4 \times 11 \times 35,
$$
when $N>0$, $\Delta_{x}=-4 N<0$. Therefore, the answer is (C).