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Quadric Surfaces Graphing in 3 Dimensions

Quadric Surfaces Graphing in 3 Dimensions. Lesson 10.2. A Point in 3D. Points graphed with respect to three axes. z. y. • (3,2 6). x. z. y. x. Graphing a Plane in 3D. Given 2x - 3y + 4z = 12 Determine intercepts z intercept when x, y = 0 y intercept when x, z = 0

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Quadric Surfaces Graphing in 3 Dimensions

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  1. Quadric SurfacesGraphing in 3 Dimensions Lesson 10.2

  2. A Point in 3D • Points graphed with respect to three axes z y • (3,2 6) x

  3. z y x Graphing a Plane in 3D • Given2x - 3y + 4z = 12 • Determine intercepts • z intercept when x, y = 0 • y intercept when x, z = 0 • x intercept when y, z = 0 3 6 -4

  4. z y x Graphing a Plane in 3D • Consider the equation x + y = 7 • z can take on any value • Results in plane … • through the line x + y = 7on the x-y plane • parallel to z axis

  5. z y x Equation of a Sphere • Given(x – a)2 + (y – b)2 + (z – c)2 = r2 • Center at (a, b, c) • radius = r c • • a b

  6. Locate This Sphere • Given • Complete the square

  7. Graphing in 3D • Solve for z • Change calculator mode to 3D graphing • Enter equation in x and y into the Z= screen

  8. Graphing in 3D • Equation gives hemisphere • note only one 3D graph at a time • Calculator takes some time to graph all the lines of the wire frame model • Image can be rotated • hold down cursor wheel for continuous rotation

  9. Graphing in 3D • Note variety of settings for graphing window • viewing angle • number of grid lines(more lines, longertime to graph) • Use F1-Format to turnaxes on/off

  10. z y x Cylinders • Consider a curve on a plane (here, x-y plane) • line through the curve, noton the plane • generates a “wall” by tracing the line along the curve • Result is a cylinder

  11. z y x Cylinders • Curve can be • parabola • hyperbola • any function

  12. Quadric Surfaces • Consider possible versions of • Sphere • Ellipsoid • Hyperbolic paraboloid • Hyperboloid (one or two sheets) • Elliptic paraboloid • See pg 683

  13. Assignment • Lesson 10.2 • Page 684 • Exercises 1, 7, 9, 13-22, 25, 33, 43

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