Quadratic interpolation with one variable minimization function

Dear Seniors,

Hope you all are doing well.

I have a couple of questions and confusuion from many days, I read alot of litrature about Ploynomial Interpolation and lagrange formula , Quadratic adaptive method, i don't know how to fit my data into code. Because I'm working on a paper, MathWorks in this link. I'm working on autonomous driving problem, I've a Cubic spline curve points, paramertize by arc-length (s).

My data points are datapoints= [292.4553 237.5450; 288.7243 241.3229; 286.8473 243.2003; 284.9452 245.0524; 283.0156 246.8757; 281.0932 248.7067; 279.220 250.5897; 277.4467 252.5631; 273.9024 256.5073; 271.6609 257.9087; 269.0973 258.5655; 266.4479 258.5782; 263.8549 258.0314; 261.4413 256.9392; 259.2712 255.4135];

xy=[292.4553 237.5450; 290.5893 239.4335; 288.7243 241.3229; 286.8473 243.2003; 284.9452 245.0524; 283.0156 246.8757; 281.0932 248.7067; 279.2220 250.5897; 277.4467 252.5631; 275.7517 254.6064; 273.9024 256.5073; 271.6609 257.9087; 269.0973 258.5655;266.4479 258.5782;263.8549 258.0314; 261.4413 256.9392; 259.2712 255.4135; 257.2198 253.7284;255.1132 252.1134; 252.9441 250.5827; 250.7702 249.0589];
arclength=sqrt((diff(xy(:,1))).^2+(diff(xy(:,2))).^2);
s=[0 cumsum(arclength')];

Here I'm using fminbnd to find get local minimizing point betwen si & si+1, but using fminbnd we have to give x1,x2 and f(x). I've x1 and x2, I don't how to initialize f(x).