SOLUTION: Find the quadratic equation of the form y=ax^2+bx+c whose graph passes through the points (2,9) (-2, 13) (1, -2)

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Question 1007156:
Find the quadratic equation of the form y=ax^2+bx+c whose graph passes through the points (2,9) (-2, 13) (1, -2)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the points to get three equation in a,b, and c.
9=a%282%29%5E2%2Bb%282%29%2Bc
1.4a%2B2b%2Bc=9
13=a%28-2%29%5E2%2Bb%28-2%29%2Bc
2.4a-2b%2Bc=13
-2=a%281%29%5E2%2Bb%281%29%2Bc
3.a%2Bb%2Bc=-2
Subtract eq. 3 from eq. 1 and 2.
4a%2B2b%2Bc-a-b-c=9-%28-2%29
4.3a%2Bb=11
and
4a-2b%2Bc-a-b-c=13-%28-2%29
3a-3b=15
5.a-b=5
Adding eq. 4 and 5,
3a%2Bb%2Ba-b=11%2B5
4a=16
a=4
Then working backwards,
5.a-b=5
4-b=5
b=-1
and finally,
3.a%2Bb%2Bc=-2
4-1%2Bc=-2
c=-5
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highlight_green%28y=4x%5E2-x-5%29
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