Interactive resource
Surfaces z = f(x, y)
Geometry. 3D graphs of z = f(x, y): rotate to see peaks, valleys, and level sets. Free interactive GeoGebra resource — adjust parameters in the browser.
Overview
3D graphs of z = f(x, y): rotate to see peaks, valleys, and level sets.
Explanation
A bivariate function graphs as a surface in space.
z = x² + y² is an elliptic paraboloid (bowl); z = x² − y² is a hyperbolic paraboloid (saddle).
Rotate to see symmetry, extrema, and contour shapes.
How to use
Drag to rotate; switch functions for different surface shapes.