I'm trying to work out what the new co-efficients for a cubic function would be if it was shifted distance p along the x axis.
I don't know why i can't seem to do it!
I can do it using f(x-p), like y=a(x-p)^3+b(x-p)^2+c(x-p)+d
but i need it so that i just have a single co-efficient for a b c and d, so when i find the roots of that equation, i find the roots=x, not the roots=x-p (i know i can just +p afters, but that doesn't work in the particular application i'm using).
I graphed a few on excel (as it's got the curve fit that displays eqns) but i can't find a relationship, more to the point I perhaps don't know how to go about it when it's more complicated than just x^3.
From what I've done, i can see there must be a standard way of creating co-efficients so that i can shift in x, if anyone can tell me how to get to there, i'd be really greatful.