Identify Graphics card

Hello, I am extremely new to Ubuntu and my question is how do I know if the OS is recognizing the GTX 770 installed in my computer? When I loaded up City Skylines the frame rate was choppy.

Run "lspci" in a terminal and there should be a listing with nvidia in the description.

It says VGA adapter, but i have an HDMI cord does that matter?

No. It should show up as VGA.

It could be the driver. Try running:
sudo apt-get install nvidia-304 nvidia-304-updates

katamari@katamari-Elanor ~ $ lspci
00:00.0 Host bridge: Intel Corporation Xeon E3-1200 v2/3rd Gen Core processor DRAM Controller (rev 09)
00:01.0 PCI bridge: Intel Corporation Xeon E3-1200 v2/3rd Gen Core processor PCI Express Root Port (rev 09)
00:14.0 USB controller: Intel Corporation 7 Series/C210 Series Chipset Family USB xHCI Host Controller (rev 04)
00:16.0 Communication controller: Intel Corporation 7 Series/C210 Series Chipset Family MEI Controller #1 (rev 04)
00:19.0 Ethernet controller: Intel Corporation 82579V Gigabit Network Connection (rev 04)
00:1a.0 USB controller: Intel Corporation 7 Series/C210 Series Chipset Family USB Enhanced Host Controller #2 (rev 04)
00:1b.0 Audio device: Intel Corporation 7 Series/C210 Series Chipset Family High Definition Audio Controller (rev 04)
00:1c.0 PCI bridge: Intel Corporation 7 Series/C210 Series Chipset Family PCI Express Root Port 1 (rev c4)
00:1c.7 PCI bridge: Intel Corporation 7 Series/C210 Series Chipset Family PCI Express Root Port 8 (rev c4)
00:1d.0 USB controller: Intel Corporation 7 Series/C210 Series Chipset Family USB Enhanced Host Controller #1 (rev 04)
00:1f.0 ISA bridge: Intel Corporation Z77 Express Chipset LPC Controller (rev 04)
00:1f.2 SATA controller: Intel Corporation 7 Series/C210 Series Chipset Family 6-port SATA Controller [AHCI mode] (rev 04)
00:1f.3 SMBus: Intel Corporation 7 Series/C210 Series Chipset Family SMBus Controller (rev 04)
01:00.0 VGA compatible controller: NVIDIA Corporation GK106 [GeForce GTX 660] (rev a1)
01:00.1 Audio device: NVIDIA Corporation GK106 HDMI Audio Controller (rev a1)
03:00.0 USB controller: ASMedia Technology Inc. ASM1042 SuperSpeed USB Host Controller
katamari@katamari-Elanor ~ $

I got this.
twacoman@twacoman-XPS-8500:~$ sudo apt-get install nvidia-304 nvidia-304-updates
[sudo] password for twacoman:
Reading package lists... Done
Building dependency tree
Reading state information... Done
nvidia-304 is already the newest version.
nvidia-304 set to manually installed.
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
nvidia-304 : Recommends: libcuda1-304 but it is not going to be installed
Recommends: nvidia-libopencl1-304 but it is not going to be installed
Recommends: nvidia-opencl-icd-304 but it is not going to be installed
Conflicts: xorg-driver-binary
nvidia-304-updates : Recommends: nvidia-libopencl1-304-updates but it is not going to be installed
Conflicts: xorg-driver-binary
E: Unable to correct problems, you have held broken packages.

follow this.
https://forum.teksyndicate.com/t/how-to-get-the-latest-nvidia-drivers-on-ubuntu-using-a-repository/76661/2
It'll get more up-to-date drivers

You should try installing the recommended packages that apt is listing.