Answer and explanation:
Infinitive phrase is a type of phrase where the main part is a verb (infinitive).
Object usually fulfills the phrase as it let us know what is affected by the action.
Modifier expands the infinitive phrase in a way that gives us an insight in what way the action is taken. Modifiers are usually adverbs.
1. to cook
expanded phrase: to cook a turkey
Sentence: I have to learn how to cook a turkey as Thanksgiving approachs.
2. to buy
expanded phrase: to buy a dress
Sentence: Mary wants to buy a dress for Tim's wedding.
3. to discover
expanded phrase: to discover something new
Sentence: Anne and John are going on vacation to South Africa, as they want to discover something new.
4. to tell
expanded phrase: to tell slowly
Sentence: He asked her to tell him slowly why she was crying.