00:01
So in this question, we'd like to sketch a graph of the surface z equals 4 minus x squared minus y squared.
00:10
And so to sketch this, i'm going to think about transformations a little bit, all right? specifically, what i'm going to do is i'm going to rewrite this a little bit.
00:20
I can say this is 4 minus the quantity of x squared plus y squared.
00:28
Or i could say this is z equals negative the quantity of x squared plus y squared plus four.
00:40
Now, you might say, well, why is that helpful to think of it in that way? because if you think back to earlier in the course, we considered the surface, z equals x squared plus y squared.
00:57
What does z equals x squared plus y squared? like.
01:02
This is what's called an elliptic paraboloid.
01:06
It's an elliptic paraboloid opening up with its vertex at the origin.
01:14
This is analogous to just y equals x squared in two -dimensional space, z equals x squared plus y squared.
01:23
Now, what do you suspect would happen if we put a negative in front of that? putting a negative in front of that is going to to make this elliptic paraboloid open downwards instead of upwards...
