Answer
Hyperbollic paraboloid.
See image:
.
Work Step by Step
Rewriting, we get
$\displaystyle \qquad \frac{z-1}{1}=\frac{y^{2}}{1^{2}}-\frac{x^{2}}{2}$
and comparing to Table 11.1, we recognize the form of
a Hyperbollic paraboloid, with the "saddle" raised up by one unit (in the z direction).
The cross sections with planes $x=k, y=k$ are parabolas; the cross section with planes $z=k$ are hyperbolas.
