surface example

3D Basin and Ridge Graph

A parabolic basin crossed by repeated ridges.

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

Teacher prompt

Which part creates repeated ridges?

The cosine term creates the repeated ridges.

min z 0.00max z 0.0056 samples

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.

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Related graphs

Open another surface page and compare shape, 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.