I think my color ink needs adjusting won't print vivid colors they appear faded, can't find my manual

To check the ink levels from the HP Photosmart Software
1. In the HP Solution Center, click Settings, point to Print Settings, and then click Printer Toolbox.
NOTE: You can also open the Printer Toolbox from the Print Properties dialog box. In the Print Properties dialog box, click the Features tab, and then click the Printer Services button.
The Printer Toolbox appears.
2. Click the Estimated Ink Level tab.
The estimated ink levels for the print cartridges appear.

Or

Print a self-test report
1. Load A4 unused plain white paper into the input tray.
2. Press and hold the Cancel button and then press the Start Copy Color button.
The product prints a self-test report, which might indicate the source of the printing problem.
3. Make sure the test patterns show a complete grid and the thick color lines are complete.
• If more than a few lines in a pattern are broken, this might indicate a problem with the nozzles. You might need to clean the print cartridges.
• If the black line is missing, faded, streaked, or shows lines, this might indicate a problem with the black or photo print cartridge in the right slot.
• If any of the color lines are missing, faded, streaked, or show lines, this might indicate a problem with the tri-color print cartridge in the left slot.

TRY TO ADJUST THE MANAGE COLOR LOCATING ON YOUR COMPUTER FIND IT AND ADJUST THE DARK COLOR

check to see if the color cartridge has the plastic tab on the cartridge. Remove and reinsert cartridge.

the printer need maintenance.
go to the following link and download the users manual and select the maintenance section.

What you are describing is a bad print head. You can try running the eliminate light stripes several times, and jet substitution, but most likely the print head will have to be replaced to remedy your problem.
You can try googling. Phaser printer print heads or phaser printheads.
There seems to be a secondary market appearing for those print heads. I can tell you from Xerox, if you have no maintenance agreement, they cost $750 per print head.
Honestly, having worked on about every type of color printer known to man, the new solid ink phaser printers, produce a dry ink image of 2400 x 2400 dpi with ink particles that align end to end. The resolution of those printers are remarkable and can be purchased for less than the price of one of those new print heads.
Now for reliable, albeit somewhat not as sharp a color image, but still exceptional, you really can not beat an HP.
The ink stick technology really no longer has the color vividness advantage it initially had. The inks that align end to end, have ended that advantage and are sure a lot cheaper to operate per page.

Clean off the bottom of your color cartridge with a slighty damp tissue to make sure the whole doesn't have ink stuck in it. If that doesn't work then its possible the ink has dried up in the cartridge and youll have to replace it. How old is the color cartridge and do you print often with it? If so if could be running low.

are your cartridges old and did you remove the protective stickers from them

Actually magenta is the weakest compared to cyan and
yellow using even K3 inks. Now epson is releasing
K3 with vivid magenta ink. Using any color management
I have found it very difficult to reach a real red without
a lot of tweaking in my color profiles. Now it appears
that Epson sees the problem and is changing magenta
out for vivid magenta ink to solve the weak magenta.