Phantom Graph 4th Degree General

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Why no Bx^3?

The third degree term in a 4th degree polynomial can be eliminated with a horizontal shift. Since phantom graphs shift with the function, we use f(x)=Ax^4+Cx^2+Dx as the general 4th degree. Adding a constant term just shifts everything up or down. Note: If g(x)=Ax^4+Bx^3+Cx^2+Dx then f(x)=g(x-h) with h=B/(3A) would have no x^3 term.