Shifted Conics: Parabolas
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 = ax2, 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!
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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: x2/a2 - y2/b2 = 1: http://youtu.be/Y6iYC4VEAi0
Hyperbola Examples: http://youtu.be/LvccUMFrY3k .
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