Answer
See image.
.
Work Step by Step
$ a.\quad$
To sketch the surface $z=f(x,y)=y^{2},$
note that:
* z is nonnegative (the surface is on or above the xy plane),
* x is ommited from the equation: the trace in $x=0$ (the yz plane) will be translated along the x axis (similar to unbounded cylinders).
The trace in the yz plane is a parabola, $z=y^{2}$,
which we translate along the x-axis into planes $x=k, k\in \mathbb{R}.$
$ b.\quad$
In the xy plane, we equate $f(x,y)$ with several values of c, resulting in
$z=y^{2}=c\qquad $(so only nonnnegative c apply)
These are parallel lines $y=\pm\sqrt{c}.$
Take $c=0,1,4,9,16$
