surface example

3D Two Peak Surface Graph

Two smooth hills separated along the x-axis.

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

Quick facts

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

What this graph represents

Each exponential term contributes one mound.

Where it appears in calculus

Useful for optimization landscapes with multiple local maxima.

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: How many main local peaks are visible?

Answer: There are two main peaks, one near x=2 and one near x=-2.

Related graphs

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

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.

Gaussian Surface

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

A smooth bell-shaped surface centered at the origin.

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

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Worksheet Export

Export graph images for classroom worksheets

How to Graph z=f(x,y)

Step-by-step guide for beginners