Question 1096703: Determine whether a quadratic model exists for the set of values below. If so, write the model.
f(0)=1, f(3)=-20,f(-1)=-4
Thank you,
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Determine whether a quadratic model exists for the set of values below. If so, write the model.
f(0)=1, f(3)=-20,f(-1)=-4
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The 3 points are not colinear --> quadratic.
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y = ax^2 + bx + c
For (-1,-4)
-4 = a - b + c for (-1,-4)
1 = 0a + 0b + c for (0,1)
-20 = 9a + 3b + c for (3,-20)
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1 = 0a + 0b + c for (0,1) --> c = 1
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a - b + 1 = -4
a - b = -5
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9a + 3b + 1 = -20
9a + 3b = -21
3a + b = -7
a - b = -5
----------------- Add
4a = -12
a = -3
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b = 2
f(x) = -3x^2 + 2x + 1
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