Hello and thanks for taking a look at my Jax guide, now Jax is a champion i like alot and i have by my experience ended at this build, this build is great for being solo top, it makes you really tanky but at the same time you are able to do alot of damage, and if you play the cards right you will be unstopable.
Here is a screenshot of my first matches with this build

I have chosen ad quintessences for this build because the build is focused on tanking but you still want to be able to deal dmg, therefore the marks are damage to.

The masteries is covering the ad that jax needs and some cd and mpenetration, the last 9 are spent in armor and hp making him tanky

Now the items are focusing really hard on making Jax tanky, but with the but because of the runes and masteries he is still able to dish out some nice damage. With the attack speed from TF you are able to make good use of your ultimates passive!

You want to skill the w up ASAP to be able to deal great damage in no time to your opponents, after that you just switch between q and e and ofc ultimate at any given oppertunity
When fighting you want to ready by pressing E, use Q to leap towards and enemy with the timing of your E going en effect, once your in the air press W, now if you have done this combo correctly you will leap to your enemy, stun and deal great damage with the help of you W, if you have got TF the attack damage and speed will help dealing some quick damage, scaring off or potentionally killing the enemy champion

I have chosen Flash and ignite/exhaust as the summoner spells
Flash: Flash is chosen because of the obvious reasons, getting away from a fight og catching up to an enemy granting you a kill
Igninte: I prefer using ignite on jax due to the extra attack damage it gives when not on cooldown because of the point we put in the first offense mastery.
Exhaust: You can also switch ignite for exhaust, the exhaust will help you get away or catch up to your opponent just like flash.

If you aren't able to reach a last hit, use your Q to leap towards the target, Jax's W also allows you to take out to minions quick before your own minions take them out.
Jax's ultimate like his W helps out taking minions out fast, so time it.

With this tank build you are able to help your team by:
Engaging fights, trieng to gain the focus of the other team, still deal good damage and if you are good you can stun alot of enemies by timing you E.

Now to sum it all up this build gives you the ability to: Dominate solo top, be a tank for the team (teamplayer wuhuuu), still be able to deal out great damage and potentionally carry your team or contribute a whole lot.
Thats all, hope you all enjoy this guide and give it the rating you think it deserves
Peace
Urimlig