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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)?
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2 Answers

|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

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