Smoothing out jumping?

Hello friends!
I’m working on a simple platformer-type game. I’ve run into a bit of a problem with the script to make the player jump. He jumps, but it is very jagged (for lack of a better word), he simply teleports upward a few units and then falls down, so it looks very unnatural. I’m stuck, and I can’t for the life of me come up with a solution, any help would be much appreciated as I am pretty new at C# and game development in general. Thank you!

using UnityEngine;
using System.Collections;

public class MoveScript : MonoBehaviour {

	protected Animator animator;

	public Vector2 speed = new Vector2(50,50);
	public float jumpSpeed = 8.0F;
	public float gravity = 20.0F;
	private Vector2 movement;
	private Vector3 moveDirection = Vector3.zero;
	private CharacterController controller;


	// Use this for initialization
	void Start () {
		controller = GetComponent<CharacterController>();
		animator = GetComponent<Animator>();
	
	}
	
	// Update is called once per frame
	void Update () {

		//This code is for running
		float inputx = Input.GetAxis ("Horizontal");
		float inputy = Input.GetAxis ("Vertical");

		movement = new Vector2 (speed.x * inputx, inputy);

		//Plays animation if the player is running
		if ((Input.GetKeyDown(KeyCode.RightArrow)) || (Input.GetKeyDown(KeyCode.LeftArrow))){
		
			animator.SetBool("isRunning", false);
		}
		if ((Input.GetKeyUp(KeyCode.RightArrow)) || (Input.GetKeyUp (KeyCode.LeftArrow))){
			animator.SetBool ("isRunning", true);
		}

		//this makes the player jump
		if(Input.GetKeyDown(KeyCode.UpArrow)){
			var y = Input.GetAxis("Vertical") + 1;
			transform.Translate(0, y, 0);
		}

			

	
	
	}

	void FixedUpdate(){
		//this is also for running
		rigidbody2D.velocity = movement;
	}
}

For smooth movement, use Vector3.Lerp(). Instead of transform.Translate, use this:

transform.position = Vector3.Lerp(transform.position, Vector3(0, y, 0), Time.deltaTime * speed);

speed is a float of how fast you want it to move. You can either make that a new variable for easy editing or replace it with a float.