i think you just answered yourself in your question
y = @(y0,a,b,NN) y0 + a*x(NN) + b*x(NN).^2; %simulate parabolic data
yDIFF = @(y0,a,b,NN) yREF - y(y0,a,b,NN); %
where instead of defining with @(y0,a,b,NN) you'd just define it with @(coefs) and then
y=@(coefs) coefs(1)+ coefs(2) * x(coefs(4)) + coefs(3) * x(coefs(4)).^2;
and if that wasn't clear, its because by making coefs# into the array = [y a b NN], by doing the above with coef(1~4) you're access y,a,b, and NN.
x= @(NN) -NN:NN; %simulate x data from -NN -> NN
y = @(y0,a,b,NN) y0 + a*x(NN) + b*x(NN).^2 ;%simulate parabolic data
yREF = y(1,2,3,10); %generate the reference array
yDIFF = @(y0,a,b,NN) yREF - y(y0,a,b,NN); %
xDATA = x(10); %use common x values
yDATA1 = y(0.85,2.1,3.2,10); %dataset 1
yDIFF1 = yDIFF(0.85,2.1,3.2,10); %differences for dataset 1
coefs1 = [0.85 2.1 3.2 10];
y2=@(coefs) coefs(1)+ coefs(2) * x(coefs(4)) + coefs(3) * x(coefs(4)).^2;
yDIFF2 = @(coefs) yREF - y2(coefs) ;%
yData2 = y2(coefs1);
yDiff2 = yDIFF2(coefs1);
[yDATA1;yData2]
[yDIFF1;yDiff2]
