The main equation is:
Say we're given the points:
Let's make the center point where we want the power series to be centered. This makes x=0, f(x)=2 because that's the y value at x=0, and f(x-2)=-6 from the leftmost point and so on. So:
Now this can be solved for b, c, d.
See what b,c,d represent is the value of the first, second, and third derivative at x=0 to substitute into the power series equation about x=0.