Question 196682: please help me solve: the cubic function whose graph is shown. (-3,0)(0,-7) (1,0) (3,0)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! please help me solve: the cubic function whose graph is shown.
(-3,0)(0,-7) (1,0) (3,0)
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Form: y = ax^3 + bx^2 + cx + d
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Substitute for x/y and solve for a,b,c,d
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(-3,0): (-3)^3a + (-3)^2b + (-3)c + d = 0
(0,-7): 0a + 0b + 0c + d = -7
(1,0) : 1a + 1b + 1c + d = 0
(3,0) : (3)^3 + (3)^2b + (3)c + d = 0
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Solve the system of 4 equations with 4 unknowns by any method you know
to get:
a = -7/9
b = 7/9
c = 7
d = -7
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Equation:
y = (-7/9)x^3 + (7/9)x^2 + 7x - 7
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Cheers,
Stan H.
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