SOLUTION: Find the quadratic function that includes the set of values below (0,9), (2,15), (4,5)

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Question 1016603: Find the quadratic function that includes the set of values below
(0,9), (2,15), (4,5)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the general form of a quadratic, y=ax%5E2%2Bbx%2Bc
9=a%280%29%5E2%2Bb%280%29%2Bc
c=9
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15=a%282%29%5E2%2Bb%282%29%2B9
4a%2B2b=6
1.2a%2Bb=3
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5=a%284%29%5E2%2Bb%284%29%2B9
16a%2B4b=-4
2.4a%2Bb=-1
So then subtracting eq. 1 from eq. 2,
4a%2Bb-2a-b=-1-3
2a=-4
a=-2
and finally,
2%28-2%29%2Bb=3
-4%2Bb=3
b=7
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y=-2x%5E2%2B7x%2B9
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