Drawing Contour Maps: Level Curves of $f(x,y)=(y-2x)^2$

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SUMMARY

The discussion focuses on drawing contour maps for the function \( f(x,y) = (y - 2x)^2 \). Participants emphasize using arbitrary positive values for \( k \) in the equation \( k = (y - 2x)^2 \) to generate level curves. The key takeaway is that for each chosen value of \( k \), the corresponding level curve can be derived by solving the equation \( y - 2x = \pm \sqrt{k} \), resulting in linear equations that represent the contours.

PREREQUISITES
  • Understanding of contour maps and level curves
  • Familiarity with basic algebra and solving equations
  • Knowledge of Cartesian coordinates
  • Experience with graphing functions
NEXT STEPS
  • Learn how to graph linear equations derived from level curves
  • Explore the concept of level curves in multivariable calculus
  • Investigate the use of graphing software like Desmos for visualizing functions
  • Study the implications of contour maps in optimization problems
USEFUL FOR

Students in mathematics, educators teaching calculus, and anyone interested in visualizing functions through contour mapping.

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draw a contour map of the function showing several level curves $f(x,y)=(y-2x)^2$

how do i do this. i know i have $k=(y-2x)^2$ but how do i use it?

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Use arbitrary positive values for $k$ and draw the resultant curve for each value.
 

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