surface example

3D Cubic Surface Graph

A cubic sheet tilted by the y term.

z = x^3 - y

Teacher prompt

Which direction has cubic growth?

The x direction has cubic growth.

min z 0.00max z 0.0056 samples

What this graph represents

The x direction bends strongly while the y direction shifts height linearly.

Where it appears in calculus

Use it to show mixed polynomial behavior.

Embed this graph

Use the Embed button in the calculator to copy a ready iframe for blogs, LMS pages, and lesson notes.

Open embed page

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.