Percy may start off a bit clumsy, but then quickly regain his composure and show his true self - a brave and kind-hearted young man. He might tell some light - hearted stories about his time with Annabeth to break the ice and make her parents like him more.
He might be a bit shy at first.
Percy could be very respectful and formal, trying to show that he's a good match for Annabeth.
Percy might be a bit on edge. He would be constantly aware of his actions and words, not wanting to mess things up. He would probably listen attentively when Annabeth's family members speak and answer their questions as honestly as he can.
In the fanfic, Percy might be really nervous when he meets Annabeth's parents. He could be worried about making a good impression. Maybe he tries to be on his best behavior, like being extra polite and respectful.
Percy tries to be on his best behavior. He listens carefully when her parents talk, and answers their questions honestly. He also makes sure to compliment their home or any work they've done. He might even offer to help with something small, like setting the table if they're having a meal together. This way, he shows that he's not only interested in Annabeth but also in being part of her family in a way.
One possibility is that Percy arrives at Annabeth's parents' place and is immediately awed by their grand home. He shakes hands with her father firmly and looks her mother in the eye. They might ask him about his adventures, and he'd share some of the less dangerous ones to make them feel at ease. Then they could all sit down for a meal, and Percy would try his best to use proper table manners, all while Annabeth is giving him encouraging looks.
Percy's anger could make his powers go a bit out of control. For example, if he's near water, the water might start churning violently as he gets mad while protecting Annabeth. He could also become more physical in his protection, standing in a very aggressive stance in front of her, almost like a wild animal guarding its mate.
She might be initially very angry. Annabeth is intelligent and perceptive, so she would likely feel betrayed that Percy thought he could deceive her. For example, if Percy lies about a mission, she could find out the truth later and confront him immediately, demanding an explanation.
In this kind of fanfiction, they might have an adventure together. Maybe they'll face a new monster that they haven't encountered before. For example, a mythical creature from a less - known part of Greek mythology.
He acts politely. He greets them with a warm smile and a firm handshake.
He would be overjoyed. It's his parents, after all.
She might initially be shocked. Annabeth is a strong character, so she could start by trying to stand up to Percy verbally, asking him why he's being so mean.