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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Shifted Conics: Parabolas
Recall from my earlier video on Shifted Conics: Ellipses (and Circles) in which we can shift an ellipse by replacing x with (x - h) and y with (y - k).
This is in fact the same procedure for shifting a parabola.
We can shift the parabola y = ax2 so that its vertex (the origin) becomes the point (h , k) as shown below:
Notice that in shifting the parabola, we just replaced x by x - h and y by y - k.
In other words, to obtain the new values (x , y) of the parabola we need to add h to every x value and add k to every y value.
If h = k = 0, then there is no shift and the vertex of the parabola is still the origin!
This one is easy. The 'Trigonometry Identity' one is much harder! Its's nice that your series is back. lol
haha yup. I follow a fairly ordered upload strategy but sometimes random topics I cover take a while. Will be trying to stay focused!
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