SOLUTION: Find the equation of the parabola, y=ax^2 + bx + c, that passes through the points (1,-2), (-2, 19) and (3,4). use the Guassian elimination

Algebra ->  Matrices-and-determiminant -> SOLUTION: Find the equation of the parabola, y=ax^2 + bx + c, that passes through the points (1,-2), (-2, 19) and (3,4). use the Guassian elimination      Log On


   

Question 980271: Find the equation of the parabola, y=ax^2 + bx + c, that passes through the points (1,-2), (-2, 19) and (3,4). use the Guassian elimination
Answer by Fombitz(32388) About Me  (Show Source):
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(1,-2):-2=a%281%29%5E2%2Bb%281%29%2Bc
1.a%2Bb%2Bc=-2
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.
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(-2,19):-2=a%28-2%29%5E2%2Bb%28-2%29%2Bc
2.4a-2b%2Bc=19
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.
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(3,4) : 4=a%283%29%5E2%2Bb%283%29%2Bc
3.9a%2B3b%2Bc=4
Subtract the first equation from second and third.
4a-2b%2Bc-a-b-c=19-%28-2%29
3a-3b=21
4.a-b=7
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9a%2B3b%2Bc-a-b-c=4-%282%29
8a%2B2b=6
5.4a%2Bb=3
Now add eq. 4 and eq. 5,
a-b%2B4a%2Bb=7%2B3
5a=10
a=2
Then,
2-b=7
-b=5
b=-5
and,
2-5%2Bc=-2
c=1
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y=2x%5E2-5x%2B1