Jinx is all about playing aggressive early. Nothing else to say, playing passive early, generally won't work in your favour in the late game.

Pros

[*] High early damage
[*] Great poke and wave clear
[*] Amazing attack spped bonus with Pow Pow,the mini gunPow Pow, the Mini Gun
[*] A well timed, and well aimed ult does Tons of Damage
[*] A great passive in team fights and when split pushing
[*] Her Flame Chompers are exceptional for engage both in team fights and in lane

Cons

[*] No disposable escape (can only use flash)
[*] Somewhat mana problems with her cannon early game
[*] Her Pow Pow,the mini gunPow Pow, the Mini Gun has quite a short range, making harass easy for most opposing AD Carries

Q - Switcheroo!

Pros

[*] The attack speed bonus from Pow Pow,the mini gunPow Pow, the Mini Gun is ridiculous. You need virtually no attack speed items for 15 minutes thanks to this
[*] The AoE damage from Fishbones, The Rocket Launcher is amazing at keeping enemies off your outer turret in lane.
[*] The attack speed bonus from Pow Pow,the mini gunPow Pow, the Mini Gun will carry over for the first 2-3 shots with Fishbones, The Rocket Launcher letting you combine amazing attack speed with overpowered AoE damage in team fights/skirmishes

Cons

[*] The mana cost from Rocket Launcher] Fishbones, The Rocket Launcher per shot is ludicrous. Avoid overusing this gun in lane to avoid going out of mana
[*] The range on Pow Pow,the mini gunPow Pow, the Mini Gun is very VERY short. Farming caster minions is very risky against a high cc lane (Vayne + Leona etc)


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W - Zap!

Pros

[*] Very good for face checking brushes with the vision
[*] Great ability to secure kills from a long range
[*] The slow is great for peel, especially with a support that has good peel (sons)
[*] The slow is also good for engagement when the enemy adc is caught with it
[*] Provides great in lane poke

Cons

[*] It is easy to dodge as it shows direction and range while being casted
[*] Doesn't help with her already below average mana problems (refer to cannon)

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E - Flame Chompers

Pros

[*] Provides great AoE crowd control both for teamfights and lane skirmishes
[*] Is a great way to catch out an out of position enemy
[*] Has a large hitbox

Cons

[*] Has a somewhat short range
[*] Is difficult to land on well positioned enemies

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R - Super Mega Death Rocket

Pros

[*] Does tons of damage
[*] Can pick off out of range enemies that are low
[*] A great kill secure as it does more damage for how low the enemy is
[*] Has a global range

Cons

[*] Like Ashe's ultimate, it is very difficult to land if fired across the entire map
[*] Isn't able to clear minion waves so isn't a problem for enemy split pushers
[*] Isn't great for initiation as it does most it's damage from the % damage

Jinx's minigun is probably the main reason people play her. It brings in totally new mechanics to be playing a champion with 2 guns, like how Jayce felt when he was new.

One of the strong points about the mini gun, is that you save valuable early game gold because you don't need to buy items like Phantom Dancer and Statikk Shiv. This gives Jinx's more money to buy core items like Bloodthirster and Infinity Edge.

I recommend using Pow Pow,the mini gunPow Pow, the Mini Gun for the majority of your game. The only time you should really use cannon is when you need wave clear or a longer range to keep away from initiators like

Zap is a great damage dealing and slowing skillshot. You can use it for multiple things like slowing, revealing, and just poking.

I recommend maxing it out second due to the reduced cooldown and better slow. I don't max it first however as the benefits from SwitcherooSwitcheroo are much more beneficial, especially in laning phase and early game.

Flame chompers is a very useful lane tool as it provides hard crowd control and can work well with high crowd control supports like Leona or Thresh.

Max it out last however as the stun time doesn't increase and it deals magic damage.

Super Mega Death RocketSuper Mega Death Rocket is one of Jinx's strongest abilities. It deals tons of damage, has a global range and a very short cooldown at level 18. With my build, you build mostly damage making this deal much much more damage.

I recommend trying to save it until the end of a team fight (as opposed for surface damage) as it does more damage based on how low the enemy is.