SOLUTION: (0,-2)(1,-1)(2,2)(3,7) What is the rule for this function and please show work.

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Question 373074: (0,-2)(1,-1)(2,2)(3,7) What is the rule for this function and please show work.
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
(0,-2)(1,-1)(2,2)(3,7)

we could use a polynomial : P(x)=ax^3+bx^2+cx-2

P(0) = -2
P(1) = a + b + c - 2 = -1
P(2) = 8a + 4b + 2c - 2 = 2
P(3) = 27a + 9b + 3c -2 = 7

a + b + c = 1
8a + 4b + 2c = 4
27a + 9b + 3c = 9

2*(1)-(2) and 3(1)-(3) gives :

-6a - 2b = -2 | times 4
-24a - 6b = -6

-2b = -2 => b = 1

-6a = -2 + 2 = 0 => a = 0
c = 1 - a - b = 1 - 1 = 0

The polynomial is : P(x) = x^2 - 2


Check :
P(1) = 1 - 2 = -1
P(2) = 4 - 2 = 2
P(3) = 9 - 2 = 7
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