SOLUTION: Find the eqaution of the parabola given the three points: (1,0),(0,-4),(2,6)

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Question 443092: Find the eqaution of the parabola given the three points: (1,0),(0,-4),(2,6)

Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
We know that
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0 = a + b +c
-4 = 0 + 0 + c
6 = 4a + 2b +c
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we know c = -4
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0 = a+b-4
6 = 4a +2b -4
==============
a + b = 4
4a + 2b = 10
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++1%5Ca+%2B+1%5Cb+=+4%2C%0D%0A++++4%5Ca+%2B+2%5Cb+=+10+%29%0D%0A++We'll use substitution. After moving 1*b to the right, we get:
1%2Aa+=+4+-+1%2Ab, or a+=+4%2F1+-+1%2Ab%2F1. Substitute that
into another equation:
4%2A%284%2F1+-+1%2Ab%2F1%29+%2B+2%5Cb+=+10 and simplify: So, we know that b=3. Since a+=+4%2F1+-+1%2Ab%2F1, a=1.

Answer: system%28+a=1%2C+b=3+%29.


So a = 1 b = 3 c =-4
So our quadratic is x^2 + 3x - 4