[Michael Reach]

I think you are adding the constant term on the wrong side of the equation.
w0*1 + w1*x^2 + w2*y^2
To get these to add up to +1 in the middle of the plot (x=0, y=0, say), we'll need w0 = -1.
Then to get negative values as x increases ( --> -1 on the right side of of the plot), we'll need w1 to be negative. And so on.