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

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

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

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.