Unless you have cable TV service with Cox, you don't need a splitter. If you do have cable TV, you'd connect a splitter near your set-top box. One coax segment would route from the splitter to the set-top box and the other segment to your Arris. Let me know if you have cable TV service for the type of splitter.
Both the Arris and Panoramic are an overkill only because of your telephone service. Meaning, the Arris and Panoramic are both Internet modems. Most subscribers only require one Internet modem. However, the Arris is the only modem capable to support both Gigablast Internet and Cox Voice (telephone service). I provide price later.
Since the Arris is your Internet modem, the Panoramic is solely your in-house router.
Your setup. The coax coming from the wall should only connect to the Arris. The Arris would have two other connections. An RJ11 cable (telephone) would connect to a nearby telephone jack. An Ethernet cable (Cat-6) would connect to the Panoramic.
The 3 port are covered with tape because your modem only supports 1 router or network. It was probably made to support 4 routers but that'd be for a business service.
You need 3 ports but the Panoramic only provides 2. You'll need to replace the Panoramic.
Price. By law, Cox has to freely loan you any equipment required for telephone service. If they issued you two Internet modems (Arris and Panoramic) but only one provides telephone service, you should not have paid for it. You are renting the Panoramic from Cox with a monthly fee. You don't need to rent routers; you can buy your own router. Therefore, buy a new router with 3-4 ports, return the Panoramic and stop the fees. If you need recommendations for a WiFi router, ask on here.
