Limiting a slider to a specific category

I’m trying to alter an existing plugin, Arconix Flexslider, which currently pulls a specified number of all recent posts. I want it to limit the posts that are pulled to a specific category, named “Featured”. Below is my best guess of where this would need to happen… This plugin is actually a widget, also.

/**
     * Widget Output
     *
     * @param type $args Display arguments including before_title, after_title, before_widget, and after_widget.
     * @param type $instance The settings for the particular instance of the widget
     * @since 0.1
     * @version 0.2
     */
    function widget( $args, $instance ) {

	extract( $args );

	/** Merge with defaults */
	$instance = wp_parse_args( ( array )$instance, $this->defaults );

	/** Before widget (defined by themes) */
	echo $before_widget;

	/** Title of widget (before and after defined by themes) */
	if( ! empty( $instance['title'] ) )
	    echo $before_title . apply_filters( 'widget_title', $instance['title'], $instance, $this->id_base ) . $after_title;

	$query_args = array(
	    'post_type' => $instance['post_type'],
	    'posts_per_page' => $instance['post_num'],
	    'meta_key' => '_thumbnail_id' /** Should pull only posts with featured images */
	);

	$flex_posts = new WP_Query( $query_args );

	if ( $flex_posts->have_posts() ) {
	    echo '<div class="flex-container">
                <div class="flexslider">
                <ul class="slides">';

                while ( $flex_posts->have_posts() ) : $flex_posts->the_post();

                    echo '<li><a href="';
                    the_permalink();
                    echo '" rel="bookmark">';
                    the_post_thumbnail( $instance['image_size'] );

		    switch( $instance['show_caption'] ) {
			case 'post title':
			    echo '<p class="flex-caption">';
			    the_title();
			    echo '</p>';
			    break;

			case 'image title':
                            global $post;
                            echo '<p class="flex-caption">' . get_post( get_post_thumbnail_id( $post->ID ) )->post_title . '</p>';
			    break;

			case 'image caption':
                            global $post;
                            echo '<p class="flex-caption">' . get_post( get_post_thumbnail_id( $post->ID ) )->post_excerpt . '</p>';
			    break;

			default:
			    break;

                    }

                    echo '</a></li>';

                endwhile;

            echo '</ul></div></div>';
        }