How to get polynomial of form ax^2+c

I am using MATLAB to fit a curve to data. I have a physics formula of the form y=ax^2+c and I am trying to determine the value of the constant a and c using the data. When I fit a second degree polynomial to the data (using polyfit), MATLAB gives me the constants a b and c of the polynomial in the form of ax^2 + bx + c. Of course, that doesn't help me find a and c for my formula. I need a polynomial of the form ax^2 + 0x + c that fits the data

Answer 1

[Matt J]

p=polyfit(x.^2,y,1);

a=p(1);
c=p(2);

Answer 2

[Walter Roberson]

Suppose you have an x vector and a y vector. Then

X = x(:);
Y = y(:);
coeffs = [X.^2, ones(size(X))] \ Y;
a = coeffs(1);
c = coeffs(2);

Answer 3

[Star Strider]

You have a linear equation, so you can use the mldivide function and an appropriately constructed design matrix to estimate the parameters:

x = 0:9;                                            % Create Data
y = 2 + 5*x.^2 + 0.1*randn(size(x));                % Create Data

B = [ones(size(x(:)))  x(:).^2]\y'                  % Estimate Parameters

B =
     2.0176
     4.9998

The ‘B’ assignment is the parameter vectors, with c=B(1) and a=B(2).