When equipment has quick draw because of Jax Unmatched, do I still need to recycle the energy to equip?

When your Equipment gains Quick-Draw from Jax, Unmatched, you do not pay the Equip cost to attach it when you play it from your hand.

Here is the breakdown of how this works:

1. Play Cost: You must still pay the Energy and Power costs printed in the top-left corner of the Equipment card to play it.
2. No Equip Cost: Because the Equipment now has Quick-Draw, it gains the triggered ability: "When you play it, attach it to a unit you control." This triggered ability attaches the Equipment for free. You do not pay the Equip cost (the cost listed in the card's text box) for this initial attachment.
3. Regarding "Recycle": You only need to "recycle" cards if the specific Equipment card you are playing has a cost that explicitly requires recycling (like Last Rites). If the Equipment's Equip cost does not involve recycling, you do not need to recycle anything.

Summary: You pay the card's play cost (Energy/Power), but you bypass the Equip cost entirely thanks to the Quick-Draw ability granted by Jax.