(a) Consider the equation y = x² - 2x. What curve does this represent in R²? Make a sketch of the curve. (b) What surface does the equation in (a) above represent in R³? Make a sketch of the surface. (c) If we now had the equation z = y²-2y, describe the features of this surface in R³, and describe how we could use the answer to (b) above to answer this question. Sketch what the surface looks like.

Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.6: Parametric Equations
Problem 2ECP
Question
(a) Consider the equation y = x² - 2x. What curve does this represent in R²? Make
a sketch of the curve.
(b) What surface does the equation in (a) above represent in R³? Make a sketch of
the surface.
(c) If we now had the equation z = y²-2y, describe the features of this surface in R³,
and describe how we could use the answer to (b) above to answer this question.
Sketch what the surface looks like.
Transcribed Image Text:(a) Consider the equation y = x² - 2x. What curve does this represent in R²? Make a sketch of the curve. (b) What surface does the equation in (a) above represent in R³? Make a sketch of the surface. (c) If we now had the equation z = y²-2y, describe the features of this surface in R³, and describe how we could use the answer to (b) above to answer this question. Sketch what the surface looks like.
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