what is the cubic functions of (1, -20), (7, -20), (2, -40), (6, -40)

Question

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Answer 1

what is the cubic functions of (1, -20), (7, -20), (2, -40), (6, -40)

There isn't one.

These coordinates satisfy a quadratic function, viz y = 4x^2 - 32x + 8.

If you try to do a curve fit using the given data, you will get a miniscule coefficient for the x^3. The other coefficeints are identical with the coefficients for the quadratic function.