What sarificial offering did the girl render to procure the miracle and what was the reasoning behind it? In the book The Bluest Eye by Toni Morrison.
The "sacrificial offering" was actually the brutal poisoning death of a dog. It was perpetrated by the local fortune teller, who also happened to be an abusive pedophile. Soaphead Church is Pecola's last resort after being raped and impregnated by her father. When she first arrives, he is inspired and actually wishes to help others, instead of taking advantage of them. Yet this quickly reverts back to a kind of impotent anger, in his realization that he can do no such thing.
He tells Pecola that he is merely an “instrument” of God, and she must perform a ritual in order to find out if God will grant her wish. He despises his landlady's dog Bob, and when Pecola comes to him asking for the miracle of blue eyes, he sees the perfect opportunity to rid himself of Bob. He gives Pecola poisoned meat to give to Bob, telling her that if the dog reacts to the meat, her eyes have become blue. Of course, the dog dies, leaving Pecola to believe that she truly does have blue eyes.
This marks her descent into madness, & in Soaphead Church's letter to God, he states that he truly pities Pecola and wishes he could perform miracles. Of course he cannot, and Pecola is left broken and alone.