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

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Question 443093: Find the eqaution of the parabola given the three points: (0,1),(2,1),(-1,4)
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
(0,1) tells us that c = 1 since 1 = 0 + 0 +c
Then 1 = 4a + 2b + 1
-1 =16a + 4b + 1
----------------------
0 = 4a + 2b
-2 = 16a + 4b
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++4%5Ca+%2B+2%5Cb+=+0%2C%0D%0A++++16%5Ca+%2B+4%5Cb+=+-2+%29%0D%0A++We'll use substitution. After moving 2*b to the right, we get:
4%2Aa+=+0+-+2%2Ab, or a+=+0%2F4+-+2%2Ab%2F4. Substitute that
into another equation:
16%2A%280%2F4+-+2%2Ab%2F4%29+%2B+4%5Cb+=+-2 and simplify: So, we know that b=0.5. Since a+=+0%2F4+-+2%2Ab%2F4, a=-0.25.

Answer: system%28+a=-0.25%2C+b=0.5+%29.


So a = -(1/4) b = 1/2 c =1
So the quadratic is -%281%2F4%29x%5E2+%2B+%281%2F2%29x+%2B+1