Answer
$ a.\quad$ The inside of the parabola $y=x^{2}$, in any plane parallel to the xy-plane, above the xy-plane.
$ b.\quad$ The region contains points outside the parabola in any plane between $z=0$ and $z=2$.
Work Step by Step
$ a.\quad$
In the xy-plane ($z=0)$, $y=x^{2}$ is a parabola, and
$y\geq x^{2}$ are points inside the parabola (the region contains the positive y-axis).
The $z\geq 0$ condition means that this parabola can be raised upward.
The region contains points inside the parabola $y=x^{2}$, in any plane parallel to the xy-plane, above the xy-plane.
$ b.\quad$
In the xy-plane ($z=0)$, $x=y^{2}$ is a parabola, and
$x\leq y^{2}$ are points outside the parabola (the region does not contain the positive x-axis).
The $0\leq z\leq 2$ condition means that this region can be raised upward to the plane $z=2$.
So the region contains points outside the parabola in any plane between $z=0$ and $z=2.$
