Her birthday cake baked by her has an octagon shape.
(The past participial phrase baked by her modifies the noun cake. The verb baked is in the past participial form, and it heads the participial phrase.)
A phrase is a group of words that functions as a single unit without a subject or a verb. Unlike a clause which contains a subject and a verb and conveys a complete idea, a phrase forms part of a clause or a sentence as it does not have a complete thought to stand on its own as an independent unit.
The predicate adjective comes after the subject that it describes. In the sentence “The puppies are getting fat”, the predicate adjective fat modifies the subject puppies, and is connected to the subject by a linking verb are.
Present Participial Phrase
A present participial phrase usually starts with a verb that is in the present participle form. It is used as an adjective to modify a noun in a sentence.
The family hoping for good weather is going horse riding.
(The present participial phrase hoping for good weather modifies the noun family. Hoping is the present participial form of the verb hope.)