graphing hyperbolic paraboloid ???

shizzy

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Aug 10, 2005
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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!
 
Hi shizzy,

shizzy said:
k = x^2 - y^2
This is a hyperbola which can be rewritten in standard form as:

hyp.png


Thus the hyperbola has vertices at
sk.png
and
msk.png
 
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