Sketching a Bowl-Shaped Surface

[anubis01]

Homework Statement

Sketch the surface x+y²+z²+1=0

Homework Equations

The Attempt at a Solution

I'm not to sure how to proceed with this. My initial idea was to re-arrange for x such that
x=-1-y²+z²=-1-r²

thus the equation for the surface becomes y²+z²=r²

I'm not sure what to do next though.

 

[benorin]

$x=y^2+z^2$ is a bowl opening which direction?
$x=1+y^2+z^2$ is the same bowl shifted one unit in which direction?
$x=-(1+y^2+z^2)=-1-y^2-z^2$ is the second bowl reflected about which axis?

 

[anubis01]

okay x=y²+z² is a bowl opening in the x direction
x=1+y²+z² is the same bowl shifted by 1 unit to the right along the x-axis

x=-1-y²-z² is the same bowl reflected along the negative x-axis.

So the image should be a bowl that runs along the positive and negative x-axis.

 

[benorin]

no picture? :(

 

[anubis01]

heres the picture I drew, I wasn't quite sure whether to draw the two bowls as connected or separated object

http://img62.imageshack.us/img62/465/cci1501201000000.jpg

 

[benorin]

$x=-(1+y^2+z^2)\le -1$ right?

 

[anubis01]

ah, so then the bowl only runs along the negative x-axis like this
http://img25.imageshack.us/img25/465/cci1501201000000.jpg