5. Given that the graph of a quadratic function opens upwards and does not pass through the origin $O$, the vertex coordinates are $(1,-2)$, it intersects the $x$-axis at points $A$ and $B$, and intersects the $y$-axis at point $C$, and satisfies the relationship $|O C|^{2}=|O A| \cdot|O B|$.
(1) Find the analytical expression of the quadratic function;
(2) Find the area of $\triangle A B C$.
(2003, Taiyuan City Junior High School Mathematics Competition)
(Answer: (1) $y=x^{2}-2 x-1$ or $y=(1+\sqrt{2}) x^{2}-$
$$
\begin{array}{l}
(2+2 \sqrt{2}) x+\sqrt{2}-1 \text {; (2) } S_{\triangle A B C}=\sqrt{2} \text { or }(\sqrt{2}-1) \cdot \\
\sqrt{2(\sqrt{2}-1)} .)
\end{array}
$$