Because $z$'s dependence on $x$ is simpler than its dependence on $y$, we plot cross-sections with three values: $x=0$, $x$ negative, and $x$ positive.

Notice that the minimal value of each parabola is $z = x$. For visual clarity, the figure is not drawn to scale.

We observe that the surface is like a parabola in $(y,z)$ that slopes along the $x$ axis. This shape is similar to a half-pipe on a ski slope. Adding shading and lines of constant $y$: