[University Calculus / Numerical Methods] Compare parabolas

I have a program where I do the following:

Suppose I have [; x_{1} ;], ..., [; x_{n} ;] points in the real plane. Let [; P ;] be the parabola fitted on these points (it doesn't pass through them, just the nearest possible). These points are consecutive positions of a moving object.

Suppose now the object's next position is [; x_{n+1} ;] . Now I fit the parabola [; Q ;] on [; x_{2} ;] , ... , [; x_{n+1} ;] .

Are there any reasonable ways of comparing the parabolas [; P ;] and [; Q ;] ? Comparing as in " [; P ;] is very different from [; Q ;] ".

My aim is to see when the moving object changes its behaviour. I am looking for a measure that doesn't depend on how flat or curved the parabolas [; P ;] and [; Q ;] are.