SOLUTION: Find a polynomial function whose graph passes through (-1,-11),(0,-6),(1,-3), and (2,4).

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Question 1057566: Find a polynomial function whose graph passes through (-1,-11),(0,-6),(1,-3), and (2,4).
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use a general cubic equation since you have 4 points.
y=ax%5E3%2Bbx%5E2%2Bcx%2Bd
(-1,-11)
-11=a%28-1%29%5E3%2Bb%28-1%29%5E2%2Bc%28-1%29%2Bd
1.-a%2Bb-c%2Bd=-11
(0,-6)
-6=a%280%29%5E3%2Bb%280%29%5E2%2Bc%280%29%2Bd
2.d=-6
(1,-3)
-3=a%281%29%5E3%2Bb%281%29%5E2%2Bc%281%29%2Bd
3.a%2Bb%2Bc%2Bd=-3
(2,4)
4=a%282%29%5E3%2Bb%282%29%5E2%2Bc%282%29%2Bd
4.8a%2B4b%2B2c%2Bd=4
Use the result from 2 on the 3 other equations,
-a%2Bb-c-6=-11
5.-a%2Bb-c=-5
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a%2Bb%2Bc-6=-3
6.a%2Bb%2Bc=3
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8a%2B4b%2B2c-6=4
8a%2B4b%2B2c=10
7.4a%2B2b%2Bc=5
Add 5 to 7 and subtract 6 from 7 to get two new equations eliminating c.
4a%2B2b%2Bc-a%2Bb-c=5-5
3a%2B3b=0
8.a%2Bb=0
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4a%2B2b%2Bc-a-b-c=5-3
9.3a%2Bb=2
Subtract 8 from 9 to eliminate b.
3a%2Bb-a-b=2-0
2a=2
a=1
So then,
1%2Bb=0
b=-1
and
1-1%2Bc=3
c=3
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y=x%5E3-x%5E2%2B3x-6