Sketch the graph and describe the vertical and horizontal traces.

Is this simply a parabola that touches ONLY the yz-plane in R^3?

It __can't__ be a parabola since it is a 2-variables function and thus is a surface in . Take, for example, the

values . Here, you get the usual parabola on the yz plane...but it is THE SAME for ANY value of x, so you actually get

a paraboloid every perpendicular to the xy-plane cut of which looks at the well-known parabola .

Go to the site Functions of Two Variables to see how this function looks.

Tonio
Would the traces basically be:

Horizontal:

Vertical: