As part of his plan to marry rich, Petruchio determines to marry Katherine, the shrew. He understands he must convince both Baptista and Kate that he will not be moved by any antics or outbursts or other shrewish behavior.
When he meets Baptista in Act II, Petruchio speaks of Katherine in glowing terms, calling her "fair" and "virtuous." He lays it on pretty thick when he says:
...hearing of her beauty and her wit,
Her affability and bashful modesty,
Her wondrous qualities and mild behaviour....
Clearly the audience has already seen this is not an accurate description of Kate; Baptista certainly knows his daughter is nothing like that. However, both of them are won over (bulldozed over?) by his apparent willingness to see beauty where others see no such thing.
Petruchio uses this same kind of language with Kate, and she is almost, or perhaps temporarily, won over as well. Petruchio does a masterful job in The Taming of the Shrew of letting everyone think he's in control.