finding the expression of cubic

**chaneliman** · February 7th 2008, 02:24 AM

it goes through the orgin and ponts are (-2,-3) (1,.75) (2,3)

thanks

**mr fantastic** · February 7th 2008, 02:56 AM

Originally Posted by chaneliman

it goes through the orgin and ponts are (-2,-3) (1,.75) (2,3)

thanks

Passes through (0, 0), symmetric and no other x-intercepts: $y = ax(x^2 + b) \Rightarrow y = ax^3 + abx \Rightarrow y = ax^3 + cx$ .

Sub (2, 3): $3 = a(2)^3 + 2c \Rightarrow 3 = 8a + 2c$ .... (1)

Sub (1, 3/4): $\frac{3}{4} = a + c$ .... (2)

Solve (1) and (2) simultaneously (use elimination method):

(1) - 2 (2): $3 - \frac{3}{2} = 8a + 2c - 2a - 2c \Rightarrow \frac{3}{2} = 6a \Rightarrow a = \frac{3}{12} = \frac{1}{4}$ .

Therefore $c = \frac{1}{2}$ .

Therefore: $y = \frac{x^3}{4} + \frac{x}{2} = \frac{1}{4} (x^3 + 2x)$

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