Obtain the standard form

$2 x^2-y^2-4 x-2 y-z\+2\=0$$\stackrel{\text{manipulate equation}}{\to }$$-{\left(y\+1\right)}^2\+2{\left(x-1\right)}^2\=z-1$ 

Obtain the equivalent of the surfaces in Figures 3.3.2(a, b)

$2 x^2-y^2-4 x-2 y-z\+2\=0$$\to$

Define $f$ so that the graph of $f\=0$ is a quadric surface

$f≔2 x^2-y^2-4 x-2 y-z\+2\:$

Complete the square and put $f$ into standard form

$\mathrm{Student}:-\mathrm{Precalculus}:-\mathrm{CompleteSquare}\left(f\=0\,\left[x\,y\right]\right)$

$\+\left(z-1\right)$

$\mathrm{rhs}\left(\right)\=\mathrm{lhs}\left(\right)$

Obtain the equivalent of the surfaces drawn in Figures 3.3.2(a, b)

$\mathrm{plots}:-\mathrm{implicitplot3d}\left(f\=0\,x\=-1..3\,y\=-5..3\,z\=-2..4\,\mathrm{style}\=\mathrm{surfacecontour}\,\mathrm{scaling}\=\mathrm{constrained}\, \mathrm{axes}\=\mathrm{frame}\,\mathrm{tickmarks}\=\left[4\,4\,6\right]\,\mathrm{orientation}\=\left[-50\,60\,0\right]\right)$