We did have my wife's daughter do an extra year although she arrived in US after almost completing grade 9 when we moved (only 6 weeks left in the school year). She would have also graduated at age 17 if she went into grade 10, although a few months older than your daughter. We elected to have her do Grade 9 again for the same reasons you are thinking - more math, science and English as well as to put her in school to graduate at a normal 18 years old. What i don't know if your daughter can do is repeat grade 12 after she already graduates from high school. That would be something to discuss with your local school system. You should call the school district. I think they would be rather helpful. If she can, it might be wise to repeat grade 12 for more math/science as well as English, and most importantly, eliminate your original question of whether she enrolls in college as in-state or foreign student as she would have graduated from a US high school. If they absolutely won't let you repeat grade 12 after graduating from her home school due to some rule it may even be worth considering not letting her complete grade 12 at home with an incomplete at the very end of the year. Again, a discussion for your present school district.