I am suppose to calculate the max and min of f(x,y,z) = x^2 - 2y + 2z^2 with the constraint function of x^2 + y^2 + z^2 = 1

I am to use Lagrange multipliers for this. When I do I get F sub y equal to -2 so how can this be set equal to zero!!! I am so confused. I also get lambda = 1 and = - y I am suppose to get max of function at 4 and min at -2 but I am really confused here.