Moving an object's shadow in a straight line below a parabola

robertbu - Yes I think you're right and I think that is how I solved it last night. I already had the travel vector so I just put down the shadow transform on that line before I did the calculation to turn it into a parabola. Here is the code from the coroutine. This is on the character who I'm moving in a parabola.

If anyone has a recommendation for doing this via Transform.translate instead of using a "new Vector3" every frame, I would appreciate it.

             while (curTime < jumpTime)
             {
                 float parabolicT = curTime * 2 - 1;
 
                 GetComponent<CircleCollider2D>().enabled = false;
 
                 Vector3 travelDirection = end - start;
                 Vector3 levelDirecteion = end - new Vector3(start.x, end.y, start.z);
                 Vector3 right = Vector3.Cross(travelDirection, levelDirecteion);
                 Vector3 up = Vector3.Cross(right, travelDirection);
                 if (end.y > start.y) up = -up;
                 Vector3 result = start + curTime * travelDirection;
                 shadow.transform.position = new Vector3(transform.position.x, result.y, -1);
                 result += ((-parabolicT * parabolicT + 1) * height) * up.normalized;
                 this.transform.position = result;
                 
 
                 curTime += Time.deltaTime + jumpSpeedMult;
 
                 yield return null;
             }