Bullet-nose curve

In mathematics, a bullet-nose curve is a unicursal quartic curve with three inflection points, given by the equation
The bullet curve has three double points in the real projective plane, at x=0 and y=0, x=0 and z=0, and y=0 and z=0, and is therefore a unicursal (rational) curve of genus zero.
If 
then
are the two branches of the bullet curve at the origin.