Hindistan´da iki haftalık bebek nadir görülen bir hastalıkla doğduğu için anne ve babası tarafından terk edildi.

neden terk edildi yerine terk etti yazmışlar? 

yardımcınız için teşşekür ederim

...

terk etmek = to abandon

terk edilmek = to be abandoned (passive)

Passive constructions are usually used when the person (subject) performing the action is not as important as the action itself (or where the object of the action is more important)  (re-written from a textbook)

Eg

The parents abandoned the baby. (Normal construction)

Here you would use terk etmek

The baby was abandoned by the parents. (Passive construction)

Here you would use terk edilmek

Both sentences have the same meaning, but the sentence structure changes where the importance is placed.

Orhan Parmuk roman yazmış. (Orhan Parmuk wrote a novel)

özne / nesne / fiil

The passive construction of this sentence would be

Orhan Parmuk tarafından roman yazılmış. (The novel was written by Orhan Parmuk)

...