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Graphing a Shifted Elliptic Paraboloid in 3D

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First published at 04:52 UTC on April 3rd, 2024.

#math
#geometry
#science

Math Easy Solutions

MES

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In this video I graph a shifted and horizontal elliptic paraboloid, which is a quadric surface that opens up along parabolic traces while the cross-section has elliptical traces. This is the same shape as in my earlier video but this time the ellipt…

GeoGebra 3D graphing calculator: https://www.geogebra.org/3d/tabys4ec

Time stamps:

- Example 8: Shifted Elliptic Paraboloid: 0:00
- Solution: Completing the square: 0:20
- Comparing equation with Table 1: 4:53
- Elliptic paraboloid is shifted and parallel to y-axis: 6:55
- Vertical traces in y = k plane are ellipses: 7:17
- Horizontal traces (and vertical x = k plane) are parabolas: 8:17
- Sketching the elliptic paraboloid: 9:39
- Graphing in GeoGebra: 11:09

Full video below:

- Cylinders and Quadric Surfaces: https://youtu.be/k4EyLr4uOUA
- HIVE video notes: https://peakd.com/hive-128780/@mes/cylinders-and-quadric-surfaces
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EfmYwT81SebJnU1Ny8Fc5u
- Infinite Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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