If I go to the homepage of the search engine I use, I can see the green lock to the left of the URL bar which indicates that I use HTTPS. Then when I input a search query in the box on the homepage, I get results, still over HTTPS. But I also set it as my default search engine in Firefox, which means I can use the URL bar to search - the way it works is, of course, when the string doesn't look like a valid URL, Firefox uses the default search engine to search for the query.
My concern is that I'm not sure if I use HTTPS throughout the whole time when I search from the URL bar. The results page for the query is served with HTTPS, but when I send my query, is it also over HTTPS? In other words, I'm not already on the homepage of that search engine but I pressed enter after entering my string to search for. So is that query string send unencrypted to my search engine of choice which THEN establishes a HTTPS connection (and that would be bad because it was send over plain HTTP), or does Firefox waits with my search query, then establishes a HTTPS connection and only then sends my query over HTTPS (obviously I hope this one is true because then what I'm searching for is send encrypted the whole time)?