ABCD is the control polygon for a cubic Bezier spline.

E is proportion t along AB,

F is proportion t along BC,

G is proportion t along CD,

H is proportion t along EF,

I is proportion t along FG

J is proportion t along HI.

The spline curve is the locus of J as t varies between 0 and 1.

Under what conditions on ABCD is the spline curve a parabola?