Three normal forms: point form y-y1=-$\frac{y1}{2a}$(x-x1), slope form y=mx-2am-$am^3$, parametric y+tx=2at+$at^3$. From an external point (h,k), normals satisfy $am^{3+}$(2a-h)m+k=0, a cubic yielding at most 3 real slopes with sum=0. Three normals exist when h>2a and the discriminant condition is met. The feet of three concurrent normals (co-normal points) at parameters t1, t2, t3 satisfy t1+t2+t3=0, making the centroid of co-normal points lie on the axis. The normal at t meets the parabola again at t'=-t-2/t. The evolute (envelope of normals) is 27$ay^2$=4(x-2a)^3, a semicubical parabola. The midpoint of TG (where tangent and normal meet the axis) is always the focus, a beautiful invariant property.