Graph problem

I'm having a little problem with the equation for a graph. I'm looking for something where the line is completely horizontal at point 1,1 and completely vertical at 0,0. So far I have y=-x^2+2x which gives a horizontal line at 1,1, but not a vertical line at point 0,0 - I don't think it can be done with a parabola, but I have no idea where to go from here. Pardon my noobishness. Some help please?

I think this would be a bijective solution:

f(x) =
    -sqrt(-x), if x <= 0
    sqrt(1-(x-1)^2), if 0 < x < 1
    1+(x-1)^2, if x >= 1