surface example

3D Valley Surface Graph

A parabolic valley tilted along the x-axis.

z = y^2 - 2*x

Teacher prompt

Which direction creates the valley curve?

The y direction creates the parabolic valley.

min z 0.00max z 0.0056 samples

What this graph represents

The y direction bends while x shifts the valley downward or upward.

Where it appears in calculus

Good for explaining directional slices.

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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.

Elliptic Paraboloid

z = x^2 + y^2

A bowl-shaped surface that opens upward.

Inverted Paraboloid

z = 12 - x^2 - y^2

A dome-shaped surface with a highest point at the center.