consider a linear regression function b1 + b2(x-xbar)+e

find the estimator and variance for b1 and b2.

My intuition tells me that they should be the same as the ols estimator

namely

b1=ybar-b2xbar

b2= (sum(x-xbar)(y-xbar))/(sum(x-xbar)^2)

var(b1)=sigma^2(sum(x^2)/(N*sum(x-xbar)^2)

var(b2)=sigma^2/(sum(x-xbar)^2)

what I tried to do is to plug in (x-xbar) instead of x in the formula but it don't make any sense to me, and it doesn't turn out anything near the OLS estimator formulas.

can someone help?... please...