Definitely! This age is a great time for more emphasis on academics, and many teens prefer homeschool because they recognize its efficiency. They can get their academic work done more quickly and have time left to play a musical instrument, practice gymnastics or basketball, serve vocational apprenticeships, pursue their own consuming interests, and generally get on with real life. In fact, many homeschoolers have been able to enter college early because they were homeschooled through high school.
Dual enrollment (attending public school part-time while homeschooling) is also an option in Utah. Some students choose to attend high school classes like algebra, drama, orchestra, debate, or journalism, and free-lance the rest of their education at home with great success. Some school districts will work with homeschooling families to arrange for class credits and a high school diploma, if desired.