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.