Character Controller smooth jump

Hi everyone, i'm currently trying to make a character controller for a mobile game i'm developing, but i'm stuck figuring out how to make a smooth jump instead of the linear i have now, i need a smooth jump, just like the basic character controller from unity does.

This is what i have:


I have a button, to make the controller jump.

This is the script snipped out

Code (CSharp):

1.  
2.  
3.  
4.     private CharacterController player;
5.  
6.     public float jumpSpeed=5f;
7.  
8.     public float gravity=8f;
9.  
10.  
11.     void Start()
12.         {
13.         player = GetComponent<CharacterController> ();
14.         }
15.      
16.     void Update()
17.     {          
18.             if (jumpButton.IsPressed())  
19.             {
20.                 if(player.isGrounded)
21.                 player.Move(new Vector3(0.0f,jumpSpeed*Time.deltaTime,0.0f));              
22.             }        
23.        }
24.  
25.        if(!player.isGrounded)
26.             player.Move(new Vector3(0.0f,gravity*Time.deltaTime,0.0f));
27.     }
28.    

How do you make a smooth, accelerated jump?

Thanks in advance

 

Why you wouldn't use Rigidbody with UseGravity?

 

I tried to use a rigidbody with gravity as well, but it goes through terrain.. and if i put a capsule collider it is just glitchy with CharacterController.Move .... i can't get it to work.. do you know how to do that?