surface example
3D Anisotropic Paraboloid Graph
A bowl that curves more sharply along y than x.
z = x^2 / 4 + y^2Teacher prompt
Which axis curves faster?
The y axis curves faster because its quadratic coefficient is larger.
min z 0.00max z 0.0056 samples
What this graph represents
Different coefficients create different curvature by direction.
Where it appears in calculus
Use it for Hessian and contour ellipse lessons.
Embed this graph
Use the Embed button in the calculator to copy a ready iframe for blogs, LMS pages, and lesson notes.
Open embed pageRelated graphs
Open another surface page and compare shape, slices, and contour behavior.
Saddle Surface
z = x^2 - y^2A 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.
Elliptic Paraboloid
z = x^2 + y^2A bowl-shaped surface that opens upward.
Inverted Paraboloid
z = 12 - x^2 - y^2A dome-shaped surface with a highest point at the center.