How can I find the equations of these cubic graphs?

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How can I find the equations of these cubic graphs as seen in the image above?

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All you need to “find” here are the values for $a$ and $b$ (or rather, $a_1, b_1, a_2, b_2$)

Hence, you plug in the points other than the origin (as that simply yields $0=0$) and you get a system of two equations each.

The first graph, for example, yields two equations: $-1=-27a+9b$ and $5=a+b$. From there, solve for the values $a$ and $b$ and substitute them into the equation.