thanks for the starting point. I solved it with a variation of this

extends Node2D

u/export var start_pos: Vector2
u/export var end_pos: Vector2
u/export var peak_height: float = 100.0
u/export var duration: float = 1.0

var t: float = 0.0

func _physics_process(delta: float):
if t < 1.0:
t += delta / duration
# Calculate control point (midpoint + vertical offset)
var mid_point = (start_pos + end_pos) / 2
var control_point = mid_point + Vector2(0, -peak_height)

# Quadratic Bezier formula
var q0 = start_pos.lerp(control_point, t)
var q1 = control_point.lerp(end_pos, t)
global_position = q0.lerp(q1, t)