Basic Examples (4) 

A hyperboloid of one sheet:

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A hyperboloid of two sheets, entered in equation form:

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Return the code used to create an ellipsoid plot:

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Now deploy that code:

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Plot a paraboloid:

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Scope (4) 

QuadricPlot3D handles degenerate quadrics.

Plot a cone:

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Plot a pair of intersecting planes:

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These are intersecting planes because the polynomial factors:

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Plot a parabolic cylinder:

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Plot some "random" quadrics:

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Possible Issues (3) 

QuadricPlot3D will return unevaluated if the argument is not discernibly a polynomial of total degree 2 in three variables:

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For some quadrics, e.g. "thin" hyperboloids of one sheet, QuadricPlot3D may show a view that obscures a part of the saddle:

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One can get different views simply by rotating using the mouse:

3D graphic objects can be large:

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One can reduce this considerably by rasterizing the 3D graphic object:

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There is good fidelity in the rasterized image (though it can no longer be rotated):

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