Q:

What is the equation of this curve? 

What would be the equation for the curve highlighted on the picture?  I would google it, however I don't even know what should I search for, since I don't know the technical name of this kind of curves, any idea?  or advise what should I look for? 

A:

Comments suggested a parabola, but I found that to be a rather poor fit (blue). 
Edit: I guess I might have made a mistake, the blue curve is a hyperbola.  Parabola would have been worse, though. 
Instead I'd go for an elliptical arc (green) or a Bézier curve (yellow, with given control points).  I did all my curve fitting manually, though, no automatic optimization involved. 

Edit: Since the answer by Martín-Blas Pérez Pinilla suggests not only a parabola, but one with a horizontal axis, here is the best fit I could manage for that.  This time, the parabola is in green, its directrix and focus in blue.  The endpoints of the curve in particular seem to fit rather poorly, which is why I'd still prefer the ellipse.