How are the glide polar and L/D ratio charts related?
Let's look at what exactly is shown by each curve:


The glide ratio curve plots glide ratio (horizontal distance divided by vertical distance) against airspeed.
The polar curve plots vertical speed against airspeed.


The x axis (airspeed) is the same for both plots, but the y axis is different. To convert one curve to the other, we need to convert glide ratio to vertical speed and vice versa.


  Note: I'm going to make a slight simplification here and assume that airspeed is the same as horizontal speed. This is not true when climbing or descending. A more accurate answer will require some trigonometry to calculate horizontal speed from airspeed. But the error introduced by this simplification is very small.



Vertical speed is simply airspeed times glide ratio.
Glide ratio is simply vertical speed divided by airspeed.


So, to make one curve out of the other:


To plot the polar curve, take a glide ratio curve and multiply it by the x coordinate (thus converting glide ratios to vertical speeds). Conceptually, as you travel outward on the x axis, you are magnifying the curve by x.
To plot a glide ratio curve, take the polar curve and divide it by the x coordinate (thus converting vertical speeds to glide ratios).


You mentioned parabolas. The polar curve is a "parabola" only in the vaguest sense that it is shaped like a parabola. It is not a precise mathematical parabola. Its exact shape is determined by extremely complicated aerodynamic factors.

All this being said, if your airplane has a published polar curve, use it, instead of deriving your own. Its values were measured and verified during flight test and you're better off using those than something you produced yourself using other data.