(This answer was updated, as the previous method using vq isn’t recognized anymore.)
Specifying the height of the video will change the quality accordingly.
example for html 5;
<iframe style="width:100%; height:800px;" src="https://www.youtube.com/embed/xxxxxxxx"></iframe>
If you don’t want to hardcode the width and height you can add a class to the iframe for css media queries.
Tested on a working server + passes the w3.org nuhtml validator.