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# 09.21 - Describe specified traces of the surface z = 4 x 2...

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[Hand out time-sheets for assignment #3] Section 10.6: Cylinders and quadric surfaces [Run demo of “Traces of a Surface”: the first two quadrics] Go back to x 2 + y 2 = 1 in 3D: What are all its traces? ..?.. Its horizontal traces are all circles. Its vertical traces are all … ..?.. pairs of vertical lines, single vertical lines, or empty. Use traces (and other kinds of mathematical reasoning) to describe the following surfaces: z = x 2 + y 2 + 1 z 2 = x 2 + y 2 z = sqrt(1 – x 2 y 2 ) Show page 747 of Instructor’s Guide

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Unformatted text preview: Describe specified traces of the surface z = 4 x 2 + y 2 : • Describe the vertical traces • Describe the horizontal traces for z > 0. • Describe the horizontal trace for z = 0. • Describe the horizontal traces for z < 0. Compare the graphs of z = x 2 + y 2 and z 2 = x 2 + y 2 by using traces. Determine the surface z 2 = x 2 + y 2 – 1 by using traces. [Didn’t do this in 2011; not enough time.] Have the students play Stewart’s Matching Game....
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09.21 - Describe specified traces of the surface z = 4 x 2...

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