If I have a YouTube video URL, is there any way to use PHP and cURL to get the associated thumbnail from the YouTube API?
You can get the video ID from the YouTube video url using parse_url ,parse_str and then insert in to the predictive urls for images. Thanks to YouTube for the predictive URLs
$videoUrl = "https://www.youtube.com/watch?v=8zy7wGbQgfw";
parse_str( parse_url( $videoUrl, PHP_URL_QUERY ), $my_array_of_vars );
$ytID = $my_array_of_vars['v']; //gets video ID
print "https://img.youtube.com/vi/$ytID/maxresdefault.jpg";
print "https://img.youtube.com/vi/$ytID/mqdefault.jpg";
print "https://img.youtube.com/vi/$ytID/hqdefault.jpg";
print "https://img.youtube.com/vi/$ytID/sddefault.jpg";
print "https://img.youtube.com/vi/$ytID/default.jpg";
You can use this tool to generate YouTube thumbnails
https://tools.tutsplanet.com/index.php/get-youtube-video-thumbnails