INSTRUCTOR: Sketch or use a graphing tool to view the graph of the cylindrical surface defined by the equation z equals y squared.

The way we can observe what this is going to look like is to notice that in the yz plane-- because there is no x component here. In the yz plane, this is a parabola. So if I were to sketch this with my x, y, and z axes, looking at the yz plane, I would have a parabola.

And because there is no restriction on the y value, no restriction in the x direction, this would just be a sheet of parabolas going in either direction. I'm going to scroll down my page. I'm going to show you what a computer-generated picture of that would look like. As you can see, it is, in fact, a sheet made up of parabolas that are centered at the origin. And in the yz plane, that is exactly what it looks like.