As Oedipus continues to question more subjects about the murder of past king Laius, more information concerning himself and his family is revealed. Jocasta pleads with him to leave it alone, only Oedipus argues against that.
OEDIPUS: Let the storm burst, my fixed resolve still holds, to learn my lineage, be it ne 'er so low…thus sprung why should I fear to trace my birth? Nothing can make me other than I am. (770-774).
Even though Oedipus learning more and more about his early life and his blood family ends up leading to his demise, he makes the decision to question and deluge into the true identity of who he is. A decision based completely on free will but ends up leading him directly to the fate he was predicted to have in the first place. Oedipus gives a speech to his people of Thebes, declaring that he will find whoever slayed Laius and will bring him to justice. He proves his determination by cursing himself if he does not find the one who committed the murder.
OEDIPUS: And on the murderer this curse I lay on him and all the partners in his guilt - wretch, may he pine in utter wretchedness! And for myself, if with my privity he gain admittance to my hearth, I pray the curse I laid on others fall on me.