SOLUTION: Write a quadratic function that fits the points (2,27) (4,61) and (7,142).

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Write a quadratic function that fits the points (2,27) (4,61) and (7,142).      Log On


   

Question 959048: Write a quadratic function that fits the points (2,27) (4,61) and (7,142).
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y=ax%5E2%2Bbx%2Bc
So,
1.27=4a%2B2b%2Bc
2.61=16a%2B4b%2Bc
3.142=49a%2B7b%2Bc
Subtract 1 from 2 and 1 from 3,
16a%2B4b%2Bc-4a%2B2b%2Bc=61-27
12a%2B2b=34
4.6a%2Bb=17
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49a%2B7b%2Bc-4a-2b-c=142-27
45a%2B5b=115
5.9a%2Bb=23
Subtract 4 from 5.
9a%2Bb-6a-b=23-17
3a=6
a=2
Then from 4,
12%2Bb=17
b=5
and finally from 1,
8%2B10%2Bc=27
c=9
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y=2x%5E2%2B5x%2B9