SOLUTION: Use a system of equations to find the parabola of the form y=ax^2+bx+c that goes through the three given points. (4,-54),(-2,-6),(-3,-19)

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Question 362847: Use a system of equations to find the parabola of the form y=ax^2+bx+c that goes through the three given points.
(4,-54),(-2,-6),(-3,-19)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y=ax%5E2%2Bbx%2Bc
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a%284%29%5E2%2Bb%284%29%2Bc=-54
1.16a%2B4b%2Bc=-54
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a%28-2%29%5E2%2Bb%28-2%29%2Bc=-6
2.4a-2b%2Bc=-6
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a%28-3%29%5E2%2Bb%28-3%29%2Bc=-19
3.9a-3b%2Bc=-19
Subtract eq. 2 from eq. 1,
16a%2B4b%2Bc-4a%2B2b-c=-54%2B6
12a%2B6b=-48
4.2a%2Bb=-8
Subtract eq. 3 from eq. 1,
16a%2B4b%2Bc-9a%2B3b-c=-54%2B19
7a%2B7b=-35
5.a%2Bb=-5
Subtract eq. 5 from eq. 4,
2a%2Bb-a-b=-8%2B5
highlight%28a=-3%29
From eq. 5,
-3%2Bb=-5
highlight%28b=-2%29
Then from eq. 2,
4%28-3%29-2%28-2%29%2Bc=-6
-12%2B4%2Bc=-6
highlight%28c=2%29