Answer
center $(3,-2)$, foci $(3,-6),(3,2)$, vertices $(3,-2-3\sqrt 2),(3,-2+3\sqrt 2)$
See graph.
Work Step by Step
1. Based on the given equation $\frac{(x-3)^2}{2}+\frac{(y+2)^2}{18}=1$, we can find center $(3,-2)$ with a vertical major axis, $a=\sqrt {18}=3\sqrt 2, b=\sqrt 2$, $c=\sqrt {a^2-b^2}=\sqrt {18-2}=4$, thus foci $(3,-2\pm4)$ or $(3,-6),(3,2)$, vertices $(3,-2\pm3\sqrt 2)$ or $(3,-2-3\sqrt 2),(3,-2+3\sqrt 2)$
2. See graph.
