Quadric Surfaces Graphing in 3 Dimensions Lesson 10.2

A Point in 3D Points graphed with respect to three axes (3,2 6) 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 x intercept when y, z = 0 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 = 7 on the x-y plane parallel to z axis z y x

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

Locate This Sphere Given Complete the square

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

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

Graphing in 3D Note variety of settings for graphing window viewing angle number of grid lines (more lines, longer time to graph) Use F1-Format to turn axes on/off

Cylinders Consider a curve on a plane (here, x-y plane) line through the curve, not on the plane generates a “wall” by tracing the line along the curve Result is a cylinder z y x

Cylinders Curve can be parabola hyperbola any function z y x

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

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