this is the IB HL maths parabola investigation. plzz help

Question

 

 

IB HL Parabola Investigation portfolio. I am stuck on part 3. SL= x2-x1, SR= x4-x3, D=abs(SL-SR).

 

Part 2: Find values of D for other parabolas of the form 2 y ax bx c , a 0, with vertices in quadrant 1,
intersected by the lines y x and y 2x . Consider various values of a, beginning with a=1
Make a conjecture about the value of D for these parabolas.

Part 3: Investigate your conjecture for any real value of a and any placement of the vertex. Refine your
conjecture as necessary, and prove it. Maintain the labeling convention used in parts 1 and 2 by
having the intersections of the first line to be 2 x and 3 x and the intersections with the second line to
be 1 x and 4 x .

I cant find a conjecture for part 3 as the D values seem random to me. HELP PLEASE