Like with functions of one variable there are certain standard graphs to

familiarize yourself with

z= x^2 +y^2 is a parabaloid opening up. If you are not familiar with this

consider the cross - sections z= constant x= constant y = constant to convincew yourself

y= x^2 + z^2 is a parabaloid whose central axis is along the y axis

so it is a parabaloid opening to the right along the y axis