Yes, your parents should receive the vaccine. In most flu seasons, older adults have more severe cases and possibly life-threatening complications. Since the injected vaccine does not contain any live virus, it cannot give anyone the flu. However, older adults may not develop as much immunity from the shot as younger people, so it is equally important that you and anyone else who regularly comes in contact with your parents (such as caretakers) also receive the flu shot. That would provide the best protection for them.
Nancy L. Mellow