YES! I am smiling here, as I homeschooled my daughter for the past five years, and have just awarded her a legitimate high school diploma last weekend. She always scored in the top 10% of the country on national exams, except physical sciences and math, where she still consistently scored above average. I kept her on college prep coursework, and aimed for a wide variety of educational coursework.
Each state has its own requirements, and some are more in tune with homeschooling than others. You can do this, Karen. It is difficult the first year or two, after that? You will relax, and the whole process will be easier to handle. Just keep it flexible while hitting the basics, and enjoy! Feel free to email me for support and ideas anytime you have doubts, set backs, or questions. BTW, I did not homeschool for religious reasons, nor because my child was not succeeding in public schools.