SOLUTION: A cubic polynomial function f has leading coefficient 2 and constant term 7. If f(1)=7 and f(2)=9, what is f(-2)?

Question 960907: A cubic polynomial function f has leading coefficient 2 and constant term 7. If f(1)=7 and f(2)=9, what is f(-2)?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A cubic polynomial function f has leading coefficient 2 and constant term 7. If f(1)=7 and f(2)=9, what is f(-2)?
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f(x) = ax^3 + bx^2 + cx + 7
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Using f(1) = 7 you get: a + b + c + 7 = 7
Using f(2) = 9 you get: 8a+4b+2c + 7 = 9
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Modify::
a + b + c = 0
4a + 2b + c = 1
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Subtract to get:
3a + b = 1
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Since a = 2, 6+b = 1
b = -5
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Solve for "c"::
2 -5 + c = 0
c = 3
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f(x) = 2x^3 -5x^2 + 3x + 7
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Ans: f(-2) = -16-20-6+7 = -35
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Cheers,
Stan H.
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