why is the switch-knife an important exhibit in evidence ?

The knife is important in a few different ways. First, the boy has an extensive list of prior offenses, including trying to slash another teenager with a knife. Second,  4th Juror explains that, on the night of the murder, the boy bought a uniquely carved switchblade knife identical to the one used in the murder. The boy claims that he lost it that night, before coming home to find his father dead. 4th Juror presents the death weapon, the “only one of its kind;” 8th Juror surprises the others by presenting an identical knife he had purchased in a pawn shop two blocks from where the boy lived a few nights prior, shattering the claim that the knife was unique and identifiable.