$re = '/(https?://.*?)(/courses/(?:\d+)/quizzes/(?:\d+))/?(?:take)?/m';
$str = 'https://k12.instructure.com/courses/651977/quizzes/1116753/take';
$subst = "\1/api/v1\2";
$result = preg_replace($re, $subst, $str);
echo "The result of the substitution is ".$result;
Please keep in mind that these code samples are automatically generated and are not guaranteed to work. If you find any syntax errors, feel free to submit a bug report. For a full regex reference for PHP, please visit: http://php.net/manual/en/ref.pcre.php