A person suffering from sickle-cell anemia may experience yellowing of the skin, swelling in the hands and feet, recurring pain, and eyesight problems. A series of blood tests and a test to identify hemoglobin types are done to diagnose whether the anemia is caused by sickle-cell anemia. Which lab test determines if a person has sickle-cell anemia, has the sickle-cell trait, or lacks the sickle-cell gene?