# Math Help - finding the expression of cubic

1. ## finding the expression of cubic

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

thanks

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