Unity bouncing ball with the same height and falling speed control

Your formula is correct.
The heightVector is the maximum height of your ball. For example if it's (0,10), then it means that your ball will go 10 meters high.
The time is simply a timer. The speed is the speed of your ball.

However, I recommend to multiply the speed by Time.deltaTime to make the bounce frame-rate independent.

Let's start writing code.
heightVector and speed have no complexity. Just create two public fields and you're done!

class Bouncer : MonoBehaviour
{
    public float Speed = 10;
    public Vector2 HeightVector = new Vector2(0,10);
}

To create a timer, you need a float variable. Then you need to add Time.deltaTime to it on every Update call.

class Bouncer : MonoBehaviour
{
    public float Speed = 10;
    public Vector2 HeightVector = new Vector2(0,10);

    float timer;
    void Update()
    {
         timer += Time.deltaTime;
    }
}

Congrats! you now have your timer!

Now you are really close to end. You just need calculate the current position of the ball and apply it to its transform.

class Bouncer : MonoBehaviour
{
    public float Speed = 10;
    public Vector3 HeightVector = new Vector3(0,10);

    float timer;
    void Update()
    {
         timer += Time.deltaTime;

         Vector3 currentPosition = HeightVector * Mathf.Abs(timer * Speed * Time.deltaTime);

         transform.position = currentPosition;
    }
}

Now you need to attach the Bouncer script to your ball and your ball should start bouncing!

Edit: If you want the ball to keep its original position and bounce from there, you need to keep the original position and append the calculated position to it:

class Bouncer : MonoBehaviour
{
    public float Speed = 10;
    public Vector3 HeightVector = new Vector3(0,10);
    Vector3 originalPosition;
    float timer;

    void Start()
    {
        originalPosition = transform.position;
    }

    void Update()
    {
         timer += Time.deltaTime;

         Vector3 currentPosition = HeightVector * Mathf.Abs(timer * Speed * Time.deltaTime);

         transform.position = originalPosition + currentPosition;
    }
}