## Thomas' Calculus 13th Edition

Rewrite as $\displaystyle \frac{z-8}{-1}=\frac{x^{2}}{1^{2}}+\frac{y^{2}}{1^{2}}$ We compare with Table 12.1 and conclude that this is an elliptical paraboloid. It opens down and the vertex is raised up 8 units (from the origin). The traces in xz and yz planes are parabolas. The traces in planes parallel to the xy plane are circles (special case of ellipses).