Does anybody know a way that I can make it such that the right half of the curve is mathematically inverse to the left half?

middle point is 0,0

left side is -1, -2

right side 1,2

I like the feeling that the right side gives, but how can i get the exact inverse on the other side?

If i break the tangents I can eyeball it, but this is for some joystick input so very small differences can be felt. I figured there must be some way to make it mathematically correct.