The traditional Jax build was based on the Trinity Force, Gunblade, and Rageblade, focusing on attack speed, AD, with a small touch of AP. What a bunch of PUSSYcats.

Jax is a late game champ, right? And what are the best late game items? Items that contain charges. Manamune and Archangel's. These items are like butterflies, they sit in the cocoon for a while, charging up their power, and BAM! They become OP late game, causing your UNDODGABLE SPELLS THAT ARE TARGET LOCKED to NUKE the enemy carries.

Difference? The traditional Jax focused on attack speed, constant DPS with burst from autos. This build has only a little bit attack speed because the passive honestly overkill already. Every item in this build works with another one in order to reap the full benefits of every single stat of every single item. It's math, trust me. We focus on getting the most AD while getting the most AP with tankiness from our health and mana in order to get:
Around 350 AP late game, Around 400 AD late game, health from banshee's, rod of ages, triforce,
armor from Atma's, MR from Banshee's, and EVEN convert the ridiculous amount of AD + AP into more Magic resist and Armor for your nuker. Top that traditional Jax.

Positives:
-your undodgable abilities will nuke and burst a carry
-this build is tankier than the traditional
-you do more burst damage than traditional Jax
-I think you can even out DPM traditional Jax

Negatives:
-weak early game, you are in a cocoon until late game where you shine
-not a lot of movement speed (but we have low cooldown flash)
-no sustain at all
-no Guardian Angel D: