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josha43
josha43
01.08.2019 • 
Mathematics

So, for an investigation i'm doing, i had to take the quadratic formula and take the inverse function in order to swap the x's and y's. i did all that as seen below: y=a(x-h) x^{2} +k y=a(x-h)^{2} +k y-k=a(x-h)^{2} (y-k)/a=(x-h)^{2} \sqrt{(y-k)/a} =x-h x=+/- \sqrt{(y-k)/a} +h therefore: y=+/- \sqrt{(x-k)/a} +h however, i have been told that i have to explain that since i swapped the x and y axes, the x-axis will really be the y-axis when i rotate the piece (volume of rotation). and i have to explain that dx is really dy because the xs and ys are swapped in order for the program to function properly. i just have no clue how to explain it. does this make any sense: in order to make the parabola open to the right, i had to inverse the parabolic equation, resulting in the equation x=+/- \sqrt{(y-k)/a} +h which maps a sideways parabola. however, the program that i was using, sketchpad, would not process the formula written in this way and therefore, in order for the program to function properly with the inverse function, i swapped the xs and ys, resulting in the following equation: y=+/- \sqrt{(x-k)/a} +h . this means that when i take the integral of this function, the dx is really a dy and when graphing, the x-axis is really representative of the y-axis.

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