SOLUTION: Algebrically, find the quadratic equation that passes through the points (-1, 0), (2,12),(-2,8)

Algebra ->  Linear-equations -> SOLUTION: Algebrically, find the quadratic equation that passes through the points (-1, 0), (2,12),(-2,8)      Log On


   

Question 374855: Algebrically, find the quadratic equation that passes through the points (-1, 0), (2,12),(-2,8)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The general equation for a quadratic is, y=ax%5E2%2Bbx%2Bc
0=a%28-1%29%5E2%2Bb%28-1%29%2Bc
1.a-b%2Bc=0
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12=a%282%29%5E2%2Bb%282%29%2Bc
2.4a%2B2b%2Bc=12
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8=a%28-2%29%5E2%2Bb%28-2%29%2Bc
3.4a-2b%2Bc=8
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Subtract eq. 1 from eq. 2,
4a%2B2b%2Bc-a%2Bb-c=12-0
3a%2B3b=12
4.a%2Bb=4
Subtract eq. 1 from eq. 3,
4a-2b%2Bc-a%2Bb-c=8-0
5.3a-b=8
Add eq. 4 and eq 5 together,
a%2Bb%2B3a-b=4%2B8
4a=12
a=3
Then from eq. 4,
3%2Bb=4
b=1
Then from eq. 1,
3-1%2Bc=0
c=-2
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highlight%28f%28x%29=3x%5E2%2Bx-2%29
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