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?

Question 1031884: 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 stanbon(75887) (Show Source): You can put this solution on YOUR website!
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?
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Form:: ax^3 + bx^2 + cx + d = f(x)
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Using f(-1) = 15: -a + b -c + d = 15
Using f(0) = 0::: 0 + 0 + 0 + d = 0
Using f(1) = -5:: a + b + c + d = -5
Using f(2) = 12::8a + 4b + 2c +d = 12
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Using d = 0 rewrite the equations:
-a + b -c = 15
a + b +c = -5
4a + 2b+c = 6
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Add the top 2 equations to get:
2b = 10
b = 5
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Substitute the bottom two equations to get:
3a + b = 11
3a = 6
a = 2
----
c = -5-a-b = -5-2-5 = -12
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Equation:
f(x) = 2x^3 + 5x^2 - 12x
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Cheers,
Stan H.
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