SOLUTION: A parabola whose axis is parallel to the y-axis passing through the points (-1,-3), (1,-2), (2,1). Find its equation.

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Question 1081567: A parabola whose axis is parallel to the y-axis passing through the points (-1,-3), (1,-2), (2,1). Find its equation.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the form,
y=ax%5E2%2Bbx%2Bc
For (-1,-3),
-3=a%28-1%29%5E2%2Bb%28-1%29%2Bc
1.a-b%2Bc=-3
For (1,-2),
-2=a%281%29%5E2%2Bb%281%29%2Bc
2.a%2Bb%2Bc=-2
For (2,1),
1=a%282%29%5E2%2Bb%282%29%2Bc
3.4a%2B2b%2Bc=1
Subtract 2 from 1,
a-b%2Bc-a-b-c=-3-%28-2%29
-2b=-1
b=1%2F2
Subtract 2 from 3,
4a%2B2b%2Bc-a-b-c=1-%28-2%29
3a%2Bb=3
3a%2B1%2F2=3
3a=5%2F2
a=5%2F6
and finally from 2,
a%2Bb%2Bc=-2
5%2F6%2B3%2F6%2Bc=-12%2F6
c=-20%2F6
c=-10%2F3
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y=%285%2F6%29x%5E2%2Bx%2F2-10%2F3
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