SOLUTION: find the quadratic model ofr each set of values. (-1,-1),(1,-3)(2,8)

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Question 342559: find the quadratic model ofr each set of values.
(-1,-1),(1,-3)(2,8)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The general quadratic equation is y=ax%5E2%2Bbx%2Bc
Use the three points to get three equations in a,b, and c.
(-1,-1):-1=a%28-1%29%5E2%2Bb%28-1%29%2Bc
1.a-b%2Bc=-1
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(1,-3):-3=a%281%29%5E2%2Bb%281%29%2Bc
2.a%2Bb%2Bc=-3
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(2,8):8=a%282%29%5E2%2Bb%282%29%2Bc
3.4a%2B2b%2Bc=8
Add eq. 1 and eq. 2,
a-b%2Bc%2Ba%2Bb%2Bc=-1-3
2a%2B2c=-4
4.a%2Bc=-2
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Double eq. 1 and add to eq. 3,
2a-2b%2B2c%2B4a%2B2b%2Bc=-2%2B8
6a%2B3c=6
5.2a%2Bc=2
Subtract eq. 4 from eq. 5,
2a%2Bc-a-c=2-%28-2%29
highlight%28a=4%29
Then work backwards,
a%2Bc=-2
4%2Bc=-2
highlight%28c=-6%29
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a%2Bb%2Bc=-3
4%2Bb-6=-3
highlight%28b=-1%29
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highlight_green%28y=4x%5E2-x-6%29
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Verify the solution by plugging the x values into the equation and comparing the y values.