surface example

3D Anisotropic Paraboloid Graph

A bowl that curves more sharply along y than x.

z = x^2 / 4 + y^2

Quick facts

  • Formula: z = x^2 / 4 + y^2
  • Category: surface
  • Tags: surface, calculus, z=f(x,y)

What this graph represents

Different coefficients create different curvature by direction.

Where it appears in calculus

Use it for Hessian and contour ellipse lessons.

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

Embed this graph

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

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Teacher prompt

Question: Which axis curves faster?

Answer: The y axis curves faster because its quadratic coefficient is larger.

Related graphs

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

Two Peak Surface

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

Two smooth hills separated along the x-axis.

Basin and Ridge

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

A parabolic basin crossed by repeated ridges.

Exponential Slope

z = exp(0.25*x) * cos(y)

A wave whose amplitude grows along x.

Ring Valley

z = (sqrt(x^2 + y^2) - 3)^2

A circular valley with a raised center and outside wall.

Smooth Cliff Surface

z = tanh(x) + 0.2*y

A smooth step blended with a gentle tilt.

Saddle Surface

z = x^2 - y^2

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

Explore more tools

Use these free browser tools to extend your graphing workflow.

3D Surface Plotter

Plot z=f(x,y), rotate, and export

Embed Builder

Create ready-to-use iframe embeds

Worksheet Export

Export graph images for classroom worksheets

How to Graph z=f(x,y)

Step-by-step guide for beginners