how to fit a curve to 3 points automatically?

Guys, I'd like to find an automatic method for fitting y=-x^2 curve to three points x=[12 67 16]; can any one suggest me a matlab code please?

[Torsten]

1. Points usually have x- and y-coordinates. So what do you mean by "three points x=[12 67 16]" ?

2. Your function y=-x^2 is explicitly given. So what do you mean by "fitting" if no degree of freedom for fitting exists within the function ?

Best wishes

Torsten.

[Marry M]

sorry for that, i extracted three pints with the x-y coordinates a(x1,y1), b (x2,y2) and c (x3,y3), so how can i fitt a curve like (y=-x^2) to my points?

[Ingrid]

you have not addressed Torsten's second point which is that your function is already determined

do you mean to fit y=-x^a and find a value for a? or is it y = b*x^a and you want to find the values a and b?

[Jos (10584)]

What are the parameters you want to estimate? Fitting a curve involves finding values for one or more unknown parameters, like finding A and B in the equation Yfit = A*x^2 + B that minimises the overal "distance" between the known values of y and the fitted values Yfit

[Marry M]

attached a sample what i meant, is it possible for me to find a cure like in the photo (red) fitted 3 points (back here)? if so, how? thanks alot

Answer 1

[Torsten]

Maybe something like

A=[x1^2 x1 1
   x2^2 x2 1
   x3^2 x3 1];
rhs=[y1 ; y2 ; y3];
sol=A\b;
func=@(x)sol(1)*x.^2+sol(2)*x+sol(3);
x=x1:0.1:x2;
y=func(x);
plot(x,y)

where (x1,y1), (x2,y2), (x3,y3) are the points in question ?

Best wishes

Torsten.

Answer 2

[Jos (10584)]

FT = fittype('a*x^2')
MDL = fit(x(:),y(:),FT)
MDL.a