Answer
Vertices: $( \pm 3, 0)$
and
Foci: $(\pm 1,0)$
Work Step by Step
The equation is: $ \frac{x^2}{9}+\frac{y^2}{8}=1$
The standard form of the equation of an ellipse with center $(h,k)$ with major axis and minor axis of lengths $2a$ and $2b$ is defined as:
$ \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$ or, $ \frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1$
Compare the given equation with the standard form, we get
$a=3$ and $b=2 \sqrt2$ and $c^2= a^2-b^2=3-2 \sqrt2$
or, $c=1$
Vertices: $( \pm 3, 0)$
and
Foci: $(\pm 1,0)$
See the attached graph.
