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: 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 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: . 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.