You're only calling Movie.query once, when the controller is initialized. You'll need to add a function to call Movie.query, and use that whenever the searchValue changes:
<input type="text" ng-model="searchValue" ng-change="getMovies" placeholder="Search Movie Title"/>
robotdog.controller('HomeController', function($scope, Movie) {
$scope.getMovies = function() {
$scope.movies = Movie.query({ title: $scope.searchValue });
}
});
This will call your REST api whenever the user changes the input (i.e. on keypress), so if that causes too many RPCs you may want to add a 'search' button and only issue the RPC when it's hit:
<input type="text" ng-model="searchValue"/>
<button ng-click="getMovies">Go</button>