Graphing quadratic surfaces?

Question

I am having a lot of trouble graphing quadratic surfaces. My teacher wants us to be able to identify and make rough sketches to what quadratic surfaces look like. Could any of you recommend a simplistic way of doing this? Im so used to making graphs with just the x and y coordinates system and so graphing in a x-y-z plane is very hard for me.

Answer 1

I think it's more practice...

First draw in a plane

I normally make the graphic in the xy plane where z=0, then in the xz plane where y=0 and in the yz plane where x=0

Then draw in more planes

Depending in the function you can draw when x, y or z are equal to integers, for example in x^2+y^2=z you should draw when x^2+y^2=c, and you will find is a circle.

Then draw shadows

I really don't do that, but if you can do it, the sketches will be perfect, it really isn't necessary