Find and solve?

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).

 

a+b+c=4

a+2b+4c=8

a+3b+9c=14

 

a=2, b=1, c=1

 

(1, 1, 1), (1, 2, 3), (1, 4, 9)

 

What's the answer? Is it a=2, b=1, c=1? Or (1, 1, 1), (1, 2, 3), (1, 4, 9)?

Answer 1

|1 1 1||a|....|4|

|1 2 4||b| = |8|

|1 3 9||c|....|14|

Multiply both sides by the inverse matrix,

(a, b, c)^T =

 

|1 1 1|^-1|4|

|1 2 4|..|8| = (2, 1, 1)^T

|1 3 9|..|14|

 

So, (a, b, c) = (2, 1, 1) <==Answer

Answer 2

a=2, b=1, c=1.