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I'm new to Mathematica. I'm trying to figure out how to do 3D plots that show the standard x, y, z-axes instead of a rectangle box on the outside. I looked through Wolfram's online documentation, but I was not able figure out the options/parameters needed to make this happen.

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    $\begingroup$ use the options Boxed -> False, Axes -> True, and AxesOrigin -> {0, 0, 0}? $\endgroup$ – kglr Jul 15 at 2:20
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to do it you can set the option Boxed with value false in your Plot3D function.

Plot3D[{4 + x^2 - y^2, -4 - x^2 + y^2}, {x, -2, 2}, {y, -2, 2}, 
 PlotTheme -> "Detailed", FaceGrids -> None, Boxed -> False]

Example: enter image description here

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