Append the following parameter to the Youtube-URL:
144p: &vq=tiny
240p: &vq=small
360p: &vq=medium
480p: &vq=large
720p: &vq=hd720
For instance:
src="http://www.youtube.com/watch?v=oDOXeO9fAg4"
becomes:
src="http://www.youtube.com/watch?v=oDOXeO9fAg4&vq=large"
I found that as of May, 2012, if you set the frame size so that the minimum pixel area (width • height) is above a certain threshold, it bumps the quality up from 360p to 480p, if you're video is at least 640 x 360.
I've discovered that setting a frame size to 780 x 480 for the embed frame triggers the 480p quality, without distorting the video (scaling up). 640 x 585 also works in this manner. I also used the &hd=1 parameter, but I doubt this has much control if your video is not uploaded in HD (720p or higher).
For instance:
<iframe width="780" height="480" src="http://www.youtube.com/embed/[VIDEO-ID]?rel=0&fs=1&showinfo=0&autohide=1&hd=1"></iframe>
Of course, the drawback is that by setting these static frame dimensions, you will most likely get black bars on the sides or above and below, depending on what you prefer.
If you didn't care about the controls being cut-off, you could go on to use CSS and overflow: hidden to crop the black bars out of the frame, providing you know the exact dimensions of the video.
Hope this helps, and hope the Embed method soon gets discrete quality parameters again one day!
You can also use for 1080 hd values:
240p: &vq=small , 360p: &vq=medium , 480p: &vq=large , 720p: &vq=hd720 , &vq=hd1080
You can use the YouTube JavaScript player API, which has a feature on its own to set playback quality.
player.setPlaybackQuality(suggestedQuality:String):Void
This function sets the suggested video quality for the current video. The function causes the video to reload at its current position in the new quality. If the playback quality does change, it will only change for the video being played. Calling this function does not guarantee that the playback quality will actually change. However, if the playback quality does change, the onPlaybackQualityChange event will fire, and your code should respond to the event rather than the fact that it called the setPlaybackQuality function. [source]
You can use the fmt= parameter and fill the value based on the following table :
http://en.wikipedia.org/wiki/YouTube#Quality_and_codecs
Ex : your URL would become :
http://www.youtube.com/embed/FqRgAs0SOpU?fmt=35
Source: Stackoverflow.com