Showing single category on custom home page

I am running WP 2.3.1 with a custom home page, where I need to display a list of the four most recent posts within a certain category (“announcements”).

Here is the code I’m using so far, but it doesn’t select for category:

$news = $wpdb->get_results("
	SELECT
		ID,
		post_title,
		post_date,
		post_content
	FROM $wpdb->posts
	WHERE
		post_status='publish'
	ORDER BY ID DESC LIMIT 4");
foreach($news as $np){
	[display results here]
}

How could I modify this query to display only results from a single category? My server is running MySQL 5.0, if that matters.