Shifted Conics: Example 1: Parabola

In this video I go over an example on shifting conic sections and this time shift the parabola y = 2x² – 4x + 1. Since this function is not in “standard” form, we can make it thus by completing the square to remove the x¹ 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 = 2x² 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!

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

Related Videos:

Shifted Conics: Hyperbolas: https://youtu.be/Evz6duQ2-U8
Shifted Conics: Parabolas: https://youtu.be/UlrAkAW3T8Y
Shifted Conics: Ellipses (and Circles): https://youtu.be/ZqtUfaQbj7U
Conic Sections: Hyperbola: Definition and Formula: https://youtu.be/UBIHovXNV9U
Conic Sections: Parabolas: Definition and Formula: https://youtu.be/kCJjXuuIqbE
Conic Sections: Ellipses: Definition and Derivation of Formula (Including Circles): https://youtu.be/9dETsJ2tz_M .

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