1. Help with parameterizing

Can someone give me direction on where to begin with parameterizing the function of f(x,y) = x^2+y^2-x-y. I know that x = r cos t, y = sin t and r = z. the shape of this function is a paraboloid. I believe that the function in the x-y planes would be a circle. that being said, I think I can say (cos t, sin t, ?t^2?). Any help or direction would be greatful.

2. $(x-1/2)^2 - 1/4 + (y-1/2)^2 - 1/4=f(x,y)$

$(x-1/2)^2 +(y-1/2)^2 =f(x,y)+1/2$

$(x-1/2)^2 +(y-1/2)^2 =\sqrt{f(x,y)+1/2}^2$

You can see the cross sections are circles which are centered in (1/2,1/2).

Why you need to parametrize it?

If you want to parametrize the equations would be:

x=t, y=s, z=(t-1/2)^2 +(z-1/2)^2 - 1/2

3. Thanks for the help.

I am trying to find the max and min on an interval. I did some additional reading and found out that all I need to do is sub. X= cos t and y = sin t. From here I find the derivative, which is 2(sin t cos t - sin t cos t) + cos t - sin t = cos t - sin t. This is were I am at. I have to do some more studying before I can complete the problem.

My intial thought of find the param. was incorrect, but your insight was verry helpful.