How to Graph 3-D Equations for Calculus

Graphing 3-D equations for calculus is easy if you use an online 3-D graphing calculator. With the 3-D calculator you just enter the 3-D equation (as a function of x and y), click the graph button, and the calculator takes care of the rest. For calculus, the most common type of 3-D equations include include ellipsoids, spheres, hyperboloids and the parboloid. There are also variations of these 3-D forms such as hyperbolic paraboloids.

Instructions

    • 1

      Write the equation for the height coordinate (z) of an ellipsoid as a function of its width (x) and length (y) coordinates. Use the ellipsoid equation, z = 6*sqrt(1 - (x^2)/1 - (y^2)/2), for this example. Type the right side of this equation into the equation (function) text box of your online graphing calculator. Click the "Plot 3D Graph" function to view the 3-D cross-section of ellipsoid if you are using the livePhysics 3-D calculator listed in the reference section.

    • 2

      Write the equation for the height coordinate (z) of an elliptic paraboloid as a function of its width (x) and length (y) coordinates. Use the elliptic paraboloid equation, z = (x^2)/4 + (y^2)/9, for this example. Type the right side of this equation into the equation (function) text box of your online graphing calculator. Click the "Plot 3D Graph" function to view the 3-D cross-section of the elliptic paraboloid if you are using the livePhysics 3-D calculator listed in the reference section.

    • 3

      Write the equation for the height coordinate (z) of an hyperbolic paraboloid as a function of its width (x) and length (y) coordinates. Use the hyperboloid equation, z = (x^2)/4 - (y^2)/9, for this example. Type the right side of this equation into the equation (function) text box of your online graphing calculator. Click the "Plot 3D Graph" function to view the saddle-shaped 3-D graph if you are using the livePhysics 3-D calculator listed in the reference section.

    • 4

      Write the equation for the height coordinate (z) of a sphere as a function of its width (x) and length (y) coordinates. Use the sphere equation, z = sqrt(25 - x^2 - y^2), for this example. Type the right side of this equation into the equation (function) text box of your online graphing calculator. Click the "Plot 3D Graph" function to view the 3-D cross-section of the sphere if you are using the livePhysics 3-D calculator listed in the reference section.

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