Finding Cubic Polynomials

Question

I have an equation: y=ax^3 + bx^2 + cx + d and the list of values x = 1, 2, 3, 4 when y = 3, 4, 3, -6 respectively. In Octave, I want to:

(a) Set up a system of four equations involving a, b, c and d. For example, substituting (x, y) = (1,3) into the polynomial gives the equation 3 = a + b + c + d.

(b) Solve the system in (a).

I've been trying to find how to do this for three hours and found nothing. Any help would be appreciated

Thanks.

pstscrpt - I have to do everything in Octave, even though I could find it by hand

Answer 1

Written without any ; at end of assignements so you can see what is going on.
You problem is basically a linear system in the variables [a,b,c,d]'=z So you need to build a system A*z=y, where A is a matrix 4x4, y and z are column vector size 4

x=[1,2,3,4]'
y=[3,4,3,-6]'
A=zeros(4,4)

for i=1:4
 A(i,:)= [ x(i)^3, x(i)^2, x(i), 1]
endfor 

z=A\y

the outcome will be

z =

  -1.00000
   5.00000
  -7.00000
   6.00000