surface example

3D Elliptic Paraboloid Graph

A bowl-shaped surface that opens upward.

z = x^2 + y^2

Teacher prompt

Does this graph have a maximum or a minimum?

It has a minimum at the origin and no maximum on an unbounded domain.

min z 0.00max z 0.0056 samples

What this graph represents

Every horizontal slice is a circle, and every vertical slice is a parabola.

Where it appears in calculus

Use it to show a local minimum in multivariable calculus.

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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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.

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.