Homeschooling high school can be challenging enough to undertake with normal high school kids, but throw in a student who is significantly advanced or gifted, and some parents might be tempted to call it quits! How can you keep up with a kid who's studying statistics, anatomy and physiology, and Greek, and asking for more?! Both my sons were gifted, so I know how difficult this can be. Fortunately, there are some practical things you can do to make the process easier and more manageable.
The first strategy that I find useful is called acceleration, which means that you allow your children to work faster. This strategy requires you to let go of the whole parent-teach-the-student model, because your job is not just to teach your children; your job is to help your children learn how to teach themselves. Fortunately, there will be times when you realize your child already knows a subject, perhaps because they have learned it by osmosis, so you can spend less time on that subject.
At high school level, it's important to remember that when your child finishes a standard curriculum, you can give them high school credit for it. You don't have to make them sit in front of you, as the teacher, for 150 hours before you give them credit for a course. As soon as they're done with a curriculum and know the material, go ahead and give them the high school credit. There's no rule that requires them to spend 150 hours studying something in order to earn a credit.
You can also skip unnecessary activities in a curriculum. If your child doesn't need the activities in order to learn the information, it's okay to skip those, as long as they're learning. It's also okay to administer a pretest for a subject, and simply skip the information they already know, or you can work fast through a curriculum and find out what they know first, and then move ahead.
When you don't use acceleration, and you work at the usual standard pace that children are used to, it can induce boredom. When people tell me they're struggling with a lack of motivation in their teenagers, or their kids hate school or they're bored, often it's because their student is moving at too slow a pace.
Make sure to assess your child's level first, and begin a curriculum at the point where they will actually learn new information. In this way, you allow them to learn at their own level, and remove those artificial barriers to how much they're allowed to learn. The result will be a student who's more interested in what they're learning, and more motivated to pursue their studies.