Name: Shifted Conics: Example 1: Parabola
Uploaded: 2023-06-01T17:36:32+00:00
Duration: 8 min 54 s
Description: In this video I go over an example on shifting conic sections and this time shift the parabola y = 2x^2 – 4x + 1. Since this function is not in “standard” form, we can make it thus by completing the s

2 years ago

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In this video I go over an example on shifting conic sections and this time shift the parabola y = 2x^2 – 4x + 1. Since this function is not in “standard” form, we can make it thus by completing the square to remove the x^1 power. Factoring the 2 out and completing the square, see my earlier video for more on completing the square, we get the formula y = 2(x – 1)^2 – 1. And as shown in my earlier video on shifting conic sections, and in particular parabolas, we see that this parabola is simply the parabola y = 2x^2 but shifted so that its vertex (originally at the origin) is now at the point (1 , -1). Besides just the shift, the function is exactly the same as the unshifted parabola. This is a great video in first performing algebra to complete the square and then using this new function to be able to better see how the function is just a simpler parabola but shifted vertically and horizontally; so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh5YgDSYZXX_ofHMq9g

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/shifted-conics-example-1-parabola