Find and solve a matrix equation?

Question

The parabola y=a+bx+cx^2 goes through the points (x, y)=(1, 4) and (2, 8) and (3, 14). Find and solve a matrix equation for the unknowns (a, b, c).

Answer 1

y=a+bx+cx²  write this using each point as

4=  a+b+c      for (1,4)

8=  a+2b+4c  for (2,8)

14=a+3b+9c for (3,14)

 

The matrix equation is a 3×3 matrix,  a column of unknowns = a column vector of y's

 

1   1   1 | a       4

1   2   4 | b   =  8

1   3   9 | c       14

 

The inverse matrix is

3      -3     1

-2.5   4    -1.5

.5      -1     .5

 

The unknown coefficients are

3      -3     1      |  4                2

-2.5   4    -1.5   |  8             = 1

.5      -1     .5    |  14               1

 

The curve is y = 2 + x + x²

I have clearly not described the computation of the inverse matrix.  I was lazy and did it using MINVERSE in EXCEL