parametric example

Parametric Surface Graph: Paraboloid

A paraboloid written with radius and angle.

z = x^2 + y^2

Quick facts

  • Formula: z = x^2 + y^2
  • Category: parametric
  • Tags: parametric, surface, vector calculus

What this graph represents

Polar parameters make circular level curves explicit.

Where it appears in calculus

Good for teaching symmetry.

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.

Open embed page

Teacher prompt

Question: Which parameter controls height?

Answer: The radius parameter controls height through u squared.

Related graphs

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

Torus

z = sin(sqrt(x^2 + y^2))

A donut-shaped parametric surface used in geometry and visualization.

Mobius Strip

z = atan(y / (x + 0.001))

A one-sided strip with a half twist.

Helicoid

z = atan(y / (x + 0.001)) + 0.15*sqrt(x^2 + y^2)

A screw-like minimal surface.

Wave Sheet

z = sin(x) * cos(y)

A parametric sheet whose height is a wave product.

Ripple Disk

z = sin(sqrt(x^2 + y^2))

A circular ripple described naturally with radius and angle.

Spherical Cap

z = sqrt(max(0, 16 - x^2 - y^2))

A cap from a sphere parameterized by angles.

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 Generator

Print graph-based classroom worksheets

How to Graph z=f(x,y)

Step-by-step guide for beginners