Scratch

ContourPlot3D[x^2+y^2-z^2/4==1,{x,-4,4},{y,-4,4},{z,-8,8},Axes->True,PlotRange->All,AxesLabel->{"x","y","z"}]

Remove[x,y,z]

In-class Examples

ContourPlot3D[z==x^2,{x,-4,4},{y,-4,4},{z,-8,8},Axes->True,PlotRange->All,AxesLabel->{"x","y","z"},AxesStyle->Directive[Bold,FontFamily->"Helvetica"],PlotRange->{{-5,5},{-5,5},{-5,5}},BoxRatios->Automatic,PlotPoints->50,PlotLabel->Style["z=(x^2)",Large,FontFamily->"Al Bayan"],NormalsFunction->None,MeshFunctions->{#3&},ContourStyle->{Texture[ExampleData[{"ColorTexture","Ash"}]]}]

ContourPlot3D[y^2+z^2==1,{x,-4,4},{y,-4,4},{z,-8,8},Axes->True,PlotRange->All,AxesLabel->{"x","y","z"},PlotRange->{{-5,5},{-5,5},{-5,5}},BoxRatios->Automatic,PlotPoints->50,AxesStyle->Directive[Bold,FontFamily->"Helvetica"],PlotLabel->Style["(y^2)+(z^2)=1",Large,FontFamily->"Al Bayan"],NormalsFunction->None,MeshFunctions->{#3&},ContourStyle->{Texture[ExampleData[{"ColorTexture","Ash"}]]}]

Spheres, Ellipsoids, and Hyperboloids

Investigate the behavior of quadric surfaces of the form ±((x^2)/(a^2))±((y^2)/(b^2))±((z^2)/(c^2))=1

Manipulate[
ContourPlot3D[Sign[a]x^2/a^2+Sign[b]y^2/b^2+Sign[c]z^2/c^2==1,{x,-4,4},{y,-4,4},{z,-4,4},Axes->True,PlotRange->All,AxesLabel->{"x","y","z"},PlotRange->{{-5,5},{-5,5},{-5,5}},BoxRatios->Automatic,PlotPoints->50,AxesStyle->Directive[Bold,FontFamily->"Helvetica"],PlotLabel->Style[Sign[a]x^2/a^2+Sign[b]y^2/b^2+Sign[c]z^2/c^2==1,Large],NormalsFunction->None,MeshFunctions->{#3&},ContourStyle->{Texture[ExampleData[{"ColorTexture","Amboyna"}]]}],
{{a,1},{-4,-3,-2,-1,1,2,3,4},Setter},{{b,1},{-4,-3,-2,-1,1,2,3,4},Setter},{{c,1},{-4,-3,-2,-1,1,2,3,4},Setter}]

Paraboloids

Investigate the behavior of quadric surfaces of the form ±((x^2)/(a^2))±((y^2)/(b^2))=z

Manipulate[
ContourPlot3D[Sign[a]x^2/a^2+Sign[b]y^2/b^2==z,{x,-4,4},{y,-4,4},{z,-4,4},Axes->True,PlotRange->All,AxesLabel->{"x","y","z"},PlotRange->{{-5,5},{-5,5},{-5,5}},BoxRatios->Automatic,PlotPoints->50,PlotLabel->Style[Sign[a]x^2/a^2+Sign[b]y^2/b^2==z,Large],NormalsFunction->None,MeshFunctions->{#3&},AxesStyle->Directive[Bold,FontFamily->"Helvetica"],ContourStyle->{Texture[ExampleData[{"ColorTexture","Amboyna"}]]}],
{{a,1},{-4,-3,-2,-1,1,2,3,4},Setter},{{b,1},{-4,-3,-2,-1,1,2,3,4},Setter}]

Cone

Manipulate[ContourPlot3D[If[axis=="x",-1,1]x^2+If[axis=="y",-1,1]y^2+If[axis=="z",-1,1]z^2==0,{x,-4,4},{y,-4,4},{z,-4,4},Axes->True,PlotRange->All,AxesLabel->{"x","y","z"},PlotRange->{{-5,5},{-5,5},{-5,5}},BoxRatios->Automatic,PlotPoints->50,AxesStyle->Directive[Bold,FontFamily->"Helvetica"],PlotLabel->Style[Switch[axis,"x","-(x^2)+(y^2)+(z^2)=0","y","+(x^2)-(y^2)+(z^2)=0","z","+(x^2)+(y^2)-(z^2)=0"],Large,FontFamily->"Al Bayan"],NormalsFunction->None,MeshFunctions->{#3&},ContourStyle->{Texture[ExampleData[{"ColorTexture","Ash"}]]}],{axis,{"x","y","z"},Setter}]