surface example

3D Basin and Ridge Graph

A parabolic basin crossed by repeated ridges.

z = x^2 - cos(3*y)

Quick facts

  • Formula: z = x^2 - cos(3*y)
  • Category: surface
  • Tags: surface, calculus, z=f(x,y)

What this graph represents

The quadratic term gives global growth while cosine adds local variation.

Where it appears in calculus

Use it to discuss local and global behavior together.

How to use this graph

  1. Rotate the surface by dragging with your mouse or finger
  2. Use the Embed button to copy an <iframe> for your LMS or lesson page
  3. Click PNG to export a classroom-ready image
  4. Click Formula or LaTeX to copy the equation for your notes

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Teacher prompt

Question: Which part creates repeated ridges?

Answer: The cosine term creates the repeated ridges.

Related graphs

Explore more surface examples and compare shapes, slices, and contour behavior.

Saddle Surface

z = x^2 - y^2

A saddle surface curves up in one direction and down in the perpendicular direction.

Gaussian Surface

z = exp(-(x^2 + y^2))

A smooth bell-shaped surface centered at the origin.

Elliptic Paraboloid

z = x^2 + y^2

A bowl-shaped surface that opens upward.

Inverted Paraboloid

z = 12 - x^2 - y^2

A dome-shaped surface with a highest point at the center.

Monkey Saddle

z = x^3 - 3*x*y^2

A three-way saddle with three valleys and three ridges.

Sine Wave Surface

z = sin(x) + sin(y)

Two perpendicular sine waves combined into one surface.

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3D Surface Plotter

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How to Graph z=f(x,y)

Step-by-step guide for beginners