graphing hyperbolic paraboloid ???

[shizzy]

graph z = x^2 - y^2 for k = -2, -1, 0, 1, 2

So far:

k = x^2 - y^2

I understand this is the equation for a hyperbolic parabolid. I understand what the graph looks like. What I cannot figure out is the vertexes. I don't understand why the vertexes aren't simply the k values. The book has a graph for the answer. It doesn't have the vertex values but it distinctly shows that none of the vertexes are 2 or -2.

Note: this is calculus 4 contour lines aka level curves homework problem

Any help on figuring out the vertexes for this would be much appreciated. Thanks!

 

[Matt]

Hi shizzy,

k = x^2 - y^2

This is a hyperbola which can be rewritten in standard form as:

Thus the hyperbola has vertices at

and

 

[shizzy]

That explains it. And quickly too! Thankyou!