3D Hyperbolic Valley Graph
A saddle-like surface formed by multiplying x and y.
z = x*yQuick facts
- Formula: z = x*y
- Category: surface
- Tags: surface, calculus, z=f(x,y)
What this graph represents
The sign of z depends on whether x and y have matching signs.
Where it appears in calculus
It is a simple way to teach quadrants in 3D.
How to use this graph
- Rotate the surface by dragging with your mouse or finger
- Use the Embed button to copy an
<iframe>for your LMS or lesson page - Click PNG to export a classroom-ready image
- 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 pageTeacher prompt
Question: Where is z positive?
Answer: z is positive when x and y have the same sign.
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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.
Monkey Saddle
z = x^3 - 3*x*y^2A three-way saddle with three valleys and three ridges.
Sine Wave Surface
z = sin(x) + sin(y)Two perpendicular sine waves combined into one surface.
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