12.6 Graphing Surfaces

Use ContourPlot3D

We will learn more about contours in Chapter 14.

Note the double == sign within the equation.
You need to specify a domain for x, y, and z. If it doesn’t seem to fit, then adjust those values.

Quadric Surface Example

((x^2)/16)-((y^2)/16)+z=0
hyperbolic paraboloid

ContourPlot3D[x^2/16-y^2/16+z==0,{x,-5,5},{y,-5,5},{z,-5,5}]

ContourPlot3D[x^2/16-y^2/16+z==0,{x,-5,5},{y,-5,5},{z,-5,5},AxesOrigin->{0,0,0},ContourStyle->Orange,Mesh->None,Boxed->False]

Cylinder Examples

(x^2)+(z^2)==4
circular cylinder along y-axis

ContourPlot3D[x^2+z^2==4,{x,-3,3},{y,-3,3},{z,-3,3}]

ContourPlot3D[x^2+z^2==4,{x,-3,3},{y,-3,3},{z,-3,3},AxesOrigin->{0,0,0},ContourStyle->Purple,Mesh->None,Boxed->False]

y==sin(3 x)
sinusoidal cylinder along z-axis

ContourPlot3D[y==Sin[3x],{x,-3,3},{y,-3,3},{z,-3,3},AxesOrigin->{0,0,0},ContourStyle->Yellow,Mesh->None,Boxed->False]

Abby Brown
www.abbymath.com