An infinitive phrase is a group of words introduced by "an infinitive", This group of words may function as a noun, adjective or adverb. In the following example the infinitive phrase is working as an adjective, since it modifies the noun "topic".
<em>The best </em><u><em>topic</em></u><em> </em><u><em>to write about</em></u><em> </em><em>is one you know well.</em>
<em> noun infinitive phrase</em>
Topic: Buying Food
One day, I quickly ran to the market to grab some grub(food). I slowly grabbed the bag of chips from the isles and happily skipped to the counter. The cashier quietly awaited for the payment. I furiously looked into my pockets for my money. Quickly scattering my pockets I've come to noticed I had no money. I quickly raced outside the door, throwing the food on the floor. I sadly cried thinking how i lost my money.
Hope this helps, made it on the spot :)