ParametricPlot3D[{u,v,(u^2 - v^2)},{u,-1,1},{v,-1,1}]

ParametricPlot3D[{u,v,(u^2 - v^2)},{u,-1,1},{v,-1,1},Mesh->False]

ParametricPlot3D[{u,v,(u^2 - v^2)},{u,-1,1},{v,-1,1},PlotStyle->Thickness[.05], Mesh->False,PlotPoints->40]

output1 = ParametricPlot3D[{u,v,(u^2 - v^2)/40},{u,-40,40},{v,-40,40},PlotStyle->Thickness[2], Mesh->False,PlotPoints->40]

output2 = ParametricPlot3D[{u,v,(u^3 - u v^2)/1500},{u,-40,40},{v,-40,40},PlotStyle->Thickness[2],Mesh->False,PlotPoints->40]

Export["Paraboloid.stl",output1]