Whether you qualify for any of the investor visa programs will depend on the amount of investment, your nationality, the nationality of the business, and other factors. If your parents are looking to open a subsidiary of their company in the United States, that could open up additional immigration paths for your, if you work with them. Consult an immigration familiar with investor visas when you are ready to proceed. (Avvo is not the right place to discuss your financial and immigration status in detail.)
Getting the green card through investment generally requires that the investment be $1 million or more. At best, investing in a small restaurant will get you a non-immigrant investor visa, not the green card.
You should retain an experienced immigration lawyer to review all the facts and advise you accordingly.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.