I need a math expert for an equation

So I need to make a part or attachment follow a specific path. I obviously don’t want to do it via physics because it would be very unstable, so the other option is math.

This is the path that I need the vector3 to follow.
Basically an almost straight line a the bottom, and a semicircle at the top, travelling clockwise.
Screenshot (1262)
Maybe I can use some graphing calculator? I tried Desmos but idk how to use it.

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im ngl im not even sure thats an actual real equation

iirc, in a function, x-values can’t map to more than 1 y-value

edit: yeah according to khan academy, a function doesnt map one x-value to more than one y-value like in your picture Intro to invertible functions (article) | Khan Academy

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if you drew a vertical line anywhere between the start and end of that shape, you would have 2 intersections (two y-values for one x-value)

so im not sure thats possible but then again i already forgor about invertible functions

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well what if the line at the bottom was just straight?

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They could just calculate multiple functions, one for the curved line and the other being the almost straight line.

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How would you do that?

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Maybe something like y = sqrt(r^2 -x^2) for the top semi circle and then some sort of domain restricted(?) parabola for the bottom

So I managed to port the red line into a script, but it doesn’t do negatives. Also I don’t think I can see the whole line of math for the blue.