Answer
center $(3,-1)$, foci $(3,-1-\sqrt {5}),(3,-1+\sqrt {5})$, vertices $(3,-4),(3,2)$
See graph.
Work Step by Step
1. Based on the given equation $\frac{(x-3)^2}{4}+\frac{(y+1)^2}{9}=1$, we can find center $(3,-1)$ with a vertical major axis, $a=3, b=2$, $c=\sqrt {a^2-b^2}=\sqrt {9-4}=\sqrt {5}$, thus foci $(3,-1\pm\sqrt {5})$ or $(3,-1-\sqrt {5}),(3,-1+\sqrt {5})$, vertices $(3,-1\pm3)$ or $(3,-4),(3,2)$
2. See graph.
