How Can MATLAB Calculate Polynomial Coefficients for Given Points?

[George3]

Homework Statement

`Suppose it is known that the graph of the function y= ax^2 +bx^2+cx+d passes through four given points (x_i,y_i), i = 1,2,3,4. Write a user defined function that accepts these four points as input and computes the coefficients a,b,c and d. The function should solve four linear equations in terms of the four unknowns a,b,c,and d. Test your function for the case where (x_i,y_i) = (-2,-20), (0,4), (2,68), and (4, 508), whose answer is a = 7, b = 5, c = -6, and d = 4.

Homework Equations

The Attempt at a Solution

Is there anything that can do something like a reverse polyval? Any ideas?

 

[CEL]

Replace each pair x_i, y_i in the equation. You will have four equations with the unknowns a, b, c, d.

 

[Mene]

I would suggest using the polyfit function in Matlab to find the coefficients of a polynomial that fits the given points. This function takes in the x and y values of the points and the degree of the polynomial (in this case, degree 3) and returns the coefficients in the form of a vector. You can then use the polyval function to evaluate the polynomial at any given point. This approach is more efficient and accurate than solving four linear equations manually.