i somehow have a talent where i can see the most optimal way of playing a champion with minimal play (lol jk this is just what i think is the most optimal and seems like to me)
jayce is one of the three champions with form/range changing ultimates, and unlike nidalee and elise, he has good ad scaling (unlike ad nidalee) and has a very different play-style.
EQ is the most common and basic thing that a jayce can do. the percentage increase makes q really really good to max, and with e being nerfed back then, not worth it to max it anymore, as it doesn't do as much damage as EQ and doesn't make EQ do more damage in ranged form. EQ is most used for poke, but it's part of the optimal jayce combo.
optimal jayce combo is EQ>run through gate>R right as you run through>Q>basic>basic until they start to get away>E
it'd be best if you could land the basic from mercury hammer's first attack, but it's not completely necessary and would most likely be used to last hit, as that's more important at the time. but here's a breakdown:
EQ does tons of damage just loving do it
running through the gate makes it double useful and makes you fast enough with R to catch up to the other person
Q is a gapcloser
basic attack does a good amount of damage in hammertime form
more basics for more damage
E does more damage
with both Q and E maxed, this should bring an adc to about 2/5 health before E (with BT trinity force), and the slow from hammertime Q will allow you to basic attack until you can E for the kill (or forget up and cry about it)