Quadric Surfaces

Circular Paraboloid z = (x^2) + (y^2)

Define Function

f[x_,y_]:=x^2 + y^2;

3D Surface Plot - Standard Style

Plot3D[f[x,y],{x,-2,2},{y,-2,2}, AxesLabel->{"X","Y","Z"}, 
PlotLabel->"Plot of Surface z = f[x,y] = (x^2) + (y^2)",BaseStyle->Directive[FontSize->16, FontFamily->"Times"], BoxRatios->Automatic]

3D Surface Plot - Hue Color Function Option

Plot3D[f[x,y],{x,-2,2},{y,-2,2}, AxesLabel->{"X","Y","Z"}, PlotLabel->"Plot of Surface z = f[x,y] = (x^2) + (y^2)", ColorFunction->Hue,BaseStyle->Directive[FontSize->16, FontFamily->"Times"], BoxRatios->Automatic]

3D Surface Plot - TemperatureMap Color Function Option

Plot3D[f[x,y],{x,-2,2},{y,-2,2}, AxesLabel->{"X","Y","Z"}, PlotLabel->"Plot of Surface z = f[x,y] = (x^2) + (y^2)", ColorFunction->"TemperatureMap",BaseStyle->Directive[FontSize->16, FontFamily->"Times"], BoxRatios->Automatic]

Contour Plot of z=f(x,y)

ContourPlot[f[x,y],{x,-2,2},{y,-2,2}, FrameLabel->{"X","Y"}, PlotLabel->"Contour Plot for Surface z = (x^2) + (y^2)", ColorFunction->Hue, Contours -> 40,BaseStyle->Directive[FontSize->16, FontFamily->"Times"]]

3D Surface Plot and Contour Plot using RegionFunction restriction to elliptical domain

Plot3D[f[x,y],{x,-2,2},{y,-2,2}, AxesLabel->{"X","Y","Z"}, PlotLabel->"Plot of Surface z = f[x,y] = (x^2) + (y^2)", ColorFunction->Function[{x,y,z},Hue[z]], RegionFunction->Function[{x,y,z},x^2+y^2≤ 3],BaseStyle->Directive[FontSize->16, FontFamily->"Times"], BoxRatios->Automatic]


ContourPlot[f[x,y],{x,-3,3},{y,-3,3}, FrameLabel->{"X","Y"}, PlotLabel->"Contours of z = f[x,y] = (x^2) + \!(y^2)", ColorFunction->Hue, RegionFunction->Function[{x,y,z},x^2+y^2≤ 8], Contours->40,BaseStyle->Directive[FontSize->16, FontFamily->"Times"]]

Elliptical Paraboloid z = (x^2) + 2(y^2)

Define Function

f[x_,y_]:=x^2 + 2y^2;

3D Surface Plot - Standard Style

Plot3D[f[x,y],{x,-2,2},{y,-2,2}, AxesLabel->{"X","Y","Z"}, 
PlotLabel->"Plot of Surface z = f[x,y] = (x^2) + 2(y^2)",BaseStyle->Directive[FontSize->16, FontFamily->"Times"], BoxRatios->Automatic]

3D Surface Plot - Hue Color Function Option

Plot3D[f[x,y],{x,-2,2},{y,-2,2}, AxesLabel->{"X","Y","Z"}, PlotLabel->"Plot of Surface z = f[x,y] = (x^2) + 2(y^2)", ColorFunction->Hue,BaseStyle->Directive[FontSize->16, FontFamily->"Times"], BoxRatios->Automatic]

3D Surface Plot - TemperatureMap Color Function Option

Plot3D[f[x,y],{x,-2,2},{y,-2,2}, AxesLabel->{"X","Y","Z"}, PlotLabel->"Plot of Surface z = f[x,y] = (x^2) + 2(y^2)", ColorFunction->"TemperatureMap",BaseStyle->Directive[FontSize->16, FontFamily->"Times"], BoxRatios->Automatic]

Contour Plot of z=f(x,y)

ContourPlot[f[x,y],{x,-2,2},{y,-2,2}, FrameLabel->{"X","Y"}, PlotLabel->"Contour Plot for Surface z = (x^2) + 2(y^2)", ColorFunction->Hue, Contours -> 40,BaseStyle->Directive[FontSize->16, FontFamily->"Times"]]

3D Surface Plot and Contour Plot using RegionFunction restriction to elliptical domain

Plot3D[f[x,y],{x,-2,2},{y,-Sqrt[2],Sqrt[2]}, AxesLabel->{"X","Y","Z"}, PlotLabel->"Plot of Surface z = f[x,y] = (x^2) + 2(y^2)", ColorFunction->Function[{x,y,z},Hue[z]], RegionFunction->Function[{x,y,z},x^2+2y^2≤ 4],BaseStyle->Directive[FontSize->16, FontFamily->"Times"], BoxRatios->Automatic]


ContourPlot[f[x,y],{x,-2,2},{y,-Sqrt[2],Sqrt[2]},  FrameLabel->{"X","Y"}, PlotLabel->"Contours of z = f[x,y] = (x^2) + 2(y^2)", ColorFunction->Hue, RegionFunction->Function[{x,y,z},x^2+2y^2≤ 4], Contours->60,BaseStyle->Directive[FontSize->16, FontFamily->"Times"],AspectRatio->Automatic]