equation for parabola --> Equation for parabolic basin

Question

I have a parabolic basin which i am trying to find the equation for so I can reproduce it. I have taken $3$ points along one line of it to find the equation of the parabola, and I'm wondering if there is a way I can go from this to the equation of the parabolic basin. The equation I have for the parabola is:

$y = 0.1x^2+0.3 $

($b= 0$ so no $x$ term).

I understand the equation of a parabolic basin takes the form:

$z = ax^2 + by^2$ or somehting those lines.

Any help would be appreciated.

Answer 1

as far as I know this equation $a = x^2 + y^2$ is for a circle.

http://www.wolframalpha.com/input/?i=plot+x%5E2%2B+y%5E2%3D25

Answer 2

$ 4 f z = (x^2+y^2) $ is equation of a rotationally symmetric paraboloid rotated about z-axis, f is focal length of parabola section in x-z or y-z planes.