[javascript] in angularjs how to access the element that triggered the event?

There is a solution using $element in the controller if you don't want to create another directive for this problem:

appControllers.controller('YourCtrl', ['$scope', '$timeout', '$element',
        function($scope, $timeout, $element) {

    $scope.updateTypeahead = function() {
       // ... some logic here
       $timeout(function() {
           $element[0].getElementsByClassName('search-query')[0].focus();
           // if you have unique id you can use $window instead of $element:
           // $window.document.getElementById('searchText').focus();
       });
    }
}]);

And this will work with ng-change:

<input id="searchText" type="text" class="search-query" ng-change="updateTypeahead()" ng-model="searchText" />