The ProjectileController class manages the parabolic motion of a projectile using a quadratic Bezier curve for path calculation and visualization.

public class ProjectileController
{
    private Transform launchPoint, impactPoint, curveControl;
    private float velocity, peakAltitude;
    private Vector3 movementDirection = Vector3.zero;
    private Vector3[] trajectoryPoints;
    private int currentPointIndex = 5;
    private int curveSegments = 30;
    private LineRenderer pathVisualizer = null;
    private bool isInFlight = false;
    private Vector3 initialPosition = Vector3.zero;
    private Vector3 initialRotation = Vector3.zero;

    public void Setup(Transform launch, Transform control, Transform target, float projectileVelocity, float maxHeight, LineRenderer visualizer = null)
    {
        launchPoint = launch;
        curveControl = control;
        impactPoint = target;
        velocity = projectileVelocity;
        peakAltitude = maxHeight;
        pathVisualizer = visualizer;
        initialPosition = launch.position;
        initialRotation = launch.eulerAngles;
    }

    public void LaunchProjectile()
    {
        if (isInFlight) return;
        trajectoryPoints = GenerateBezierPath(launchPoint.position, curveControl.position, impactPoint.position, curveSegments);
        isInFlight = true;
    }

    public void UpdateTrajectory()
    {
        RenderPath();
        if (isInFlight)
        {
            if (currentPointIndex >= trajectoryPoints.Length)
            {
                CompleteFlight();
                return;
            }
            movementDirection = (trajectoryPoints[currentPointIndex] - launchPoint.position).normalized;
            launchPoint.LookAt(trajectoryPoints[currentPointIndex]);
            launchPoint.position += movementDirection * Time.deltaTime * velocity;
            if (Vector3.Distance(launchPoint.position, trajectoryPoints[currentPointIndex]) <= 0.5f) currentPointIndex += 1;
        }
    }

    private void CompleteFlight()
    {
        isInFlight = false;
        currentPointIndex = 5;
        launchPoint.gameObject.SetActive(false);
        launchPoint.position = initialPosition;
        launchPoint.eulerAngles = initialRotation;
        launchPoint.gameObject.SetActive(true);
    }

    private void RenderPath()
    {
        if (pathVisualizer == null) return;
        for (int i = 1; i <= curveSegments; i++)
        {
            float interpolationFactor = i / (float)curveSegments;
            Vector3 curvePosition = ComputeBezierPoint(interpolationFactor, initialPosition, curveControl.position, impactPoint.position);
            pathVisualizer.positionCount = i;
            pathVisualizer.SetPosition(i - 1, curvePosition);
        }
    }

    private Vector3 ComputeBezierPoint(float t, Vector3 startPos, Vector3 controlPos, Vector3 endPos)
    {
        float oneMinusT = 1 - t;
        float tSquared = t * t;
        float oneMinusTSquared = oneMinusT * oneMinusT;
        Vector3 position = oneMinusTSquared * startPos;
        position += 2 * oneMinusT * t * controlPos;
        position += tSquared * endPos;
        return position;
    }

    public Vector3[] GenerateBezierPath(Vector3 startPos, Vector3 controlPos, Vector3 endPos, int segments)
    {
        Vector3[] pathArray = new Vector3[segments];
        for (int i = 1; i <= segments; i++)
        {
            float t = i / (float)segments;
            Vector3 point = ComputeBezierPoint(t, startPos, controlPos, endPos);
            pathArray[i - 1] = point;
        }
        return pathArray;
    }
}

To utilize this system, create a MonoBehaviour script that initialiezs and controls the proejctile.

public class ProjectileDemo : MonoBehaviour
{
    [SerializeField] Transform launchPoint, impactPoint, curveControl;
    [SerializeField] float peakAltitude = 40;
    [SerializeField] float projectileVelocity = 30;
    [SerializeField] LineRenderer pathVisualizer;
    private ProjectileController projectile = new ProjectileController();

    private void Awake()
    {
        projectile = new ProjectileController();
        projectile.Setup(launchPoint, curveControl, impactPoint, projectileVelocity, peakAltitude, pathVisualizer);
    }

    private void Update()
    {
        if (Input.GetMouseButton(0)) { projectile.LaunchProjectile(); }
        projectile.UpdateTrajectory();
    }
}