2

In this video I go over further into shifted conics and this time shift Parabolas. The procedure for shifting parabolas is the same as that for ellipses, which I covered in my earlier video. This is done by simply replacing x and y with (x – h) and (y – k). This means that in order to obtain the basic x and y values, we need to add h to the horizontal component and k to the vertical component. Thus we effectively shift the function horizontally and vertically. For the parabola y = ax^{2}, with the vertex at the origin, this can be shifted so that the vertex is (h, k) by re-writing the formula (y – k) = a(x – h)^{2} or y = a(x – h)^{2} + k. Although this is very similar to the case for an ellipse, it is nonetheless important to understand this concept through applying it to different functions, such as in this case a parabola, so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh5Vqjg-jPzl6_SRXlw

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

Related Videos:

Shifted Conics: Ellipses (and Circles): https://youtu.be/ZqtUfaQbj7U

Equation of a Circle and it's proof: http://youtu.be/xMXYJ9UeF4I

Conic Sections: Hyperbolas: Example 2: Vertical Hyperbola: https://youtu.be/zBNSTkoEzFI

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

Hyperbola - Definition and derivation of the equation: x^{2}/a^{2} - y^{2}/b^{2} = 1: http://youtu.be/Y6iYC4VEAi0

Hyperbola Examples: http://youtu.be/LvccUMFrY3k .

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