Two curves pass through BEP. One is called as pump performance curve which is empirically established by pump manufacturer. Second is system curve which may or may not pass through BEP based on how good or bad your pipe design is. We generally use Darcy-Weisbach equation for this.
Beyond this, you have to rephrase your question in detail.
1) The equation of an inverted parabola will work reasonably well enough for most centrifugal pump curves.
Hd = Hs + aQ^2 + bQ
Hd is the pump's differential head
Hs is shutoff head, or the differential head at zero flow
Q is flowrate
a and b are curve coefficients.
2) A system curve can be approximated by
H = Hc + aQ^2
H is the system head required at flowrate Q
Hc is the static head at zero flowrate
a is a curve coefficient.
The pump and system will operate at the flowrate where the two curves intersect.
Plot both curves together on the same chart and see where the intersection is, you must plot the pump's total discharge head for each flowrate.
3) Total Discharge Head Ht = Hsuct + Hd
Hsuct = suction head, could be different for each flowrate
On a plot of the System Curve Chart from equation (2),
take each Pump Differential Head coordinate (Q, Hd) point from the pump curve and add the suction head (your first head value will be Ht = Hc + Hs to get the point (Q, Ht).
Do the same for each flowrate to get the pump's discharge head Hd for each flowrate.
Now plot the curve containing all those (Q, Hd) points on the System Curve Chart. If you have selected the right pump, the two curves will intersect above the pump's BEP flowrate.
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