Question about Creating a Best fit arch with 4 points

[Grimatoma]

Hello, I am trying to get arch equation of someones teeth by only using 4 points on the left side of the arch. I am also counting 0,0 at the vertex of the arch (the very front of the teeth). One last thing, the best fit line does not need to go though any of the points

I am having trouble on how I can even start this, Thank you for taking the time to view my question

 

[HallsofIvy]

There are an infinite number of functions that can be fit exactly to four points and even more if you are more interested in applying some other criteria but not hitting those four points exactly.

The simplest thing to do is to use polynomials. An nth degree polynomial has n+1 coefficients to be determined so a third degree polynomial, \(\displaystyle ax^3+ bx^2+ cx= d\) has four coefficients and your four points will give four equations to determine them.