SOLUTION: What is the parabola of the equation in standard form given the points (1,-1), (2,-5), (3,-7)?

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Question 1007902: What is the parabola of the equation in standard form given the points (1,-1), (2,-5), (3,-7)?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the equation,
y=ax%5E2%2Bbx%2Bc
Generate an equation with each point,
-1=a%281%29%5E2%2Bb%281%29%2Bc
1.a%2Bb%2Bc=-1
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-5=a%282%29%5E2%2Bb%282%29%2Bc
2.4a%2B2b%2Bc=-5
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-7=a%283%29%5E2%2Bb%283%29%2Bc
3.9a%2B3b%2Bc=-7
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Subtract eq. 1 from eqs. 2 and 3 to eliminate c.
4a%2B2b%2Bc-a-b-c=-5-%28-1%29
4.3a%2Bb=-4
and
9a%2B3b%2Bc-a-b-c=-7-%28-1%29
8a%2B2b=-6
5.4a%2Bb=-3
Subtract eq. 4 from eq. 5 to eliminate b,
4a%2Bb-3a-b=-3-%28-4%29
a=1
Then from eq. 4,
3%281%29%2Bb=-4
b=-7
and finally from eq. 1,
1-7%2Bc=-1
c=5
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highlight_green%28y=x%5E2-7x%2B5%29
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