SOLUTION: The polynomial f(x) has degree 3. If f(-1) = 15, f(0)= 0, f(1) = -5, and f(2) = 12, then what are the x-intercepts of the graph of f?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The polynomial f(x) has degree 3. If f(-1) = 15, f(0)= 0, f(1) = -5, and f(2) = 12, then what are the x-intercepts of the graph of f?      Log On


   

Question 1043703: The polynomial f(x) has degree 3. If f(-1) = 15, f(0)= 0, f(1) = -5, and f(2) = 12, then what are the x-intercepts of the graph of f?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the general equation,
y=ax%5E3%2Bbx%5E2%2Bcx%2Bd
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15=a%28-1%29%5E3%2Bb%28-1%29%5E2%2Bc%28-1%29%2Bd
1.-a%2Bb-c%2Bd=15
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0=a%280%29%5E3%2Bb%280%29%5E2%2Bc%280%29%2Bd
2.d=0
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-5=a%281%29%5E3%2Bb%281%29%5E2%2Bc%281%29
3.a%2Bb%2Bc=-5
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12=a%282%29%5E3%2Bb%282%29%5E2%2Bc%282%29
8a%2B4b%2B2c=12
4.4a%2B2b%2Bc=6
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Updating eq. 1,
1.-a%2Bb-c=15
Adding eq. 1 to eq. 3,
a%2Bb%2Bc-a%2Bb-c=-5%2B15
2b=10
b=5
Adding eq. 1 to eq. 4,
4a%2B2%285%29%2Bc-a%2B5-c=15%2B6
3a%2B15=21
3a=6
a=2
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So then using eq. 3,
2%2B5%2Bc=-5
c=-12
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y=2x%5E3%2B5x%5E2-12x
Now solve for
2x%5E3%2B5x%5E2-12x=0
%282x%5E2%2B5x-12%29x=0
%282x-3%29%28x%2B4%29x=0
Solve for the three zeros or look at the graph where the func tion crosses the x-axis.
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