This Jax build will focus on destroying people and capping the points as fast as possible (basicly the whole purpose of dominion). I will also introduce you into the world of hybrid-jaxing. I hope this build helps you, and altough this is my first build i hope that its good.
I still have a tip for anyone who is going 1v1 or 1v2 you need to use your abilities like this: Empower your Weapon before you jump in with Leap strike then emidiatly use your Counter Strike to dodge all their auto-attacks. Then after you stun then with Counter strike start auto-attacking and let your abilities cool down, when the enemy is leave repeat the process, if they are not this battle is yours to take. Another tip is: You're not a champion for teamfights because Jax's abilities and his passive are solely focused on Jax himself and will not help any teammembers around him. And another thing i dont recommend is leap-striking at the last second if you find yourself in a teamfight, because you will get slaughterd.

The runes I reccomend using are the allready names runes but as alternate runes you can focus on your abilities more and not that much on simple attack damage and other offensive runes.

The masteries I created are the best for being a hybrid Jax because they offer the most on the most platforms, altough you could switch it up and go 21 0 9, I do not reccomend this because then you are not the super-uber-duper pownage Jax but just a Jax.

Different from runes and masteries you can totally mix up your items and go more to the ability powers type of items because this works just fine with the runes and masteries that you've set up. Mind you tough, dont try to build a lot on armour because Jax needs simple force and attack speed.

The skill sequence i created is the best for this guide because it matches completely with your items. And it also is very usefull for the strategy i told you at the start of the guide at the introduction.

A brief summary of a good hybrid jax is: He does not travel well with other champions because he is a 1v1 or 1v2 champion, he is the best at mid-game and early-game, and Jax does have the ability to kick ***. NOW GO OUT THERE AND DO IT!