this.navCtrl.setRoot(QuizPage);

today i was working on how to navigate from one page to another page using ionic 2 and angular code in typscript, the answer is very simple by using this inside your class.

here is an example

TYPESCRIPT
import { Component } from '@angular/core';
import { NavController, NavParams } from 'ionic-angular';
import { QuizPage } from '../quiz/quiz';
/*
  Generated class for the Next page.

  See http://ionicframework.com/docs/v2/components/#navigation for more info on
  Ionic pages and navigation.
*/
@Component({
  selector: 'page-next',
  templateUrl: 'next.html'
})
export class NextPage {

  constructor(public navCtrl: NavController, public navParams: NavParams) {}

  ionViewDidLoad() {
    //console.log('ionViewDidLoad NextPage');
  }


    showNextPage(){
    	//alert('ShowHomePage');
  	this.navCtrl.setRoot(QuizPage);
  }
}
HTML: 
<button ion-button (click)="showNextPage()">Quiz Page</button>
You can find this code in C:\apachefriends\xampp\htdocs\angular2\ionic2\examples\examples under the NavigationPages branch (using git)