Answer
A parabolic cylinder.
Work Step by Step
No x in the equation. The trace in the plane x=0 (the yz plane) will be translated along the x-axis into planes x=k.
In the yz plane, we have the graph of $z=y^{2}+1,$
a parabola opening upward (along the z axis), with vertex at (0,0,1).
Translate the curve into planes x=k, to obtain a parabolic cylinder.
