SOLUTION: The graph of f (x) = ax2 + bx + c passes through the points (1, k1), (2, k2), and (3, k3). Determine a, b, and c for (A) k1=-2, k2 = 1, k3 = 6 (B) k1 = 4, k2 = 3, k3=-2 (C) k1

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Question 167529: The graph of f (x) = ax2 + bx + c passes
through the points (1, k1), (2, k2), and (3, k3). Determine a,
b, and c for
(A) k1=-2, k2 = 1, k3 = 6
(B) k1 = 4, k2 = 3, k3=-2
(C) k1 = 8, k2=-5, k3 = 4
I attempted to solve as follows:
(A)-2= a + b + c
1= a - b + c
6= 4a + 2b +c
and entering this into a matrix, but it doesn't come out right.
What am I doing wrong?
Thank you!
Debi
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
The graph of passes
through the points (1, k1), (2, k2), and (3, k3). Determine a,
b, and c for

Plug  in:





Now since the graph passes through 
then , so substitute  for  in



or



Plug  in:





Now since the graph passes through 
then , so substitute  for  in



Plug  in:





Now since the graph passes through 
then , so substitute  for  in



 or



So we have this system:




------------------------------------------------
(A) 

the system



becomes



Solve this system and get 

--------

(B) 

the system



becomes



Solve this system and get 

----------

(C) 

the system



becomes



Solve this system and get 

Edwin
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