Depending on what you want to do, mathematica may or may not be free.
If you want the action-packed, full version, then it will cost you.
However, if you are just curious what the graph z = x
2 + y
2 looks like, then you can go to
http://www.wolframalpha.com/ and type in the Plot3D command.
There is a special syntax, but it is easy: Plot3D[ f(x,y) , {x, xmin, xmax}, {y, ymin, ymax}]
Type this command into the text box that appears when you go to the link above (replacing f(x,y), xmin, xmax, ymin, and ymax with your function and domain), hit enter, and a bunch of things will come up. The first will be a 3d Graph of your function (assuming you typed everything in correctly =s).
Also, if you are a university student, there is a very large chance that you will be able to get the student version of this for free (a full version of the program which you can install on your computer).