After taking damage from an enemy champion, the next 3 spells or attacks you receive deal less damage.
WhyPress the Attack
Press the Attack synergizes well with BotRK and Jax's natural tendency to ramp damage in duels.
Jax is a solid tower diver and Triumph's big heal can make the difference between life and deal in sticky situations.
All of Jax's damage comes from his ability to auto attack repeatedly and Alacrity helps your early game trades and skirmishes massively before you're able to build any significant Attack Speed. It also allows you to opt into more defensive items so you can prolong the trade.
WhyCoup De Grace
Your rune choice here largely depends on if your laning against a tank or not. Coup De Grace is good at killing squishy champions.
If you are laning against a tank, take Cut Down.
Iron skin is a great early game rune choice into AD lane matchups. Paired with Second Wind, the extra bit of armor can be just enough to turn a fight and begin your snowball.
If you're playing into an AP matchup or heavy AP team, take Mirror Shell instead.
Bone Plating patches up some of Jax's early game weak laning power when trying to enduring any harassment.