find a cubic polynomial p(x)=a+bx+cx2+dx3

Hello, I've been given a task of;

p(x)=a+bx+cx2+dx3 with a prescribed behaviour: p(xk)=yk, for k=1,…,4

I'm asked to create the 4×1 vector v=[a,b,c,d], whose components a,b,c and d are the coefficients of the polynomial p(x)

but I don't really understand where to begin.

Answer 1

[Torsten]

p(x1) = a+b*x1+c*x1^2+d*x1^3 = y1
p(x2) = a+b*x2+c*x2^2+d*x2^3 = y2
p(x3) = a+b*x3+c*x3^2+d*x3^3 = y3
p(x4) = a+b*x4+c*x4^2+d*x4^3 = y4

So four linear equations in the unknowns a, b, c and d.

Can you take it from here ?

Best wishes

Torsten.