Does the one year limited warranty on iphone 14 cover the shattered glass on the back of the phone

Carol is 100% correct. The standard warranty covers manufactures defects in material and workmanship. A user error is not covered. That’s where Apple Care comes in. In some countries Apple Care + provides for user errors in addition to manufacturers defects. However, there is an additional charge for Apple Care and the repair may be subject to a deductible.

AppleCare Products - iPhone - Apple

According to the warranty description, I would say no. The warranty covers:

WHAT IS COVERED BY THIS WARRANTY?

Apple warrants the Apple-branded iPhone, iPad, iPod, Apple TV or HomePod hardware product and the Apple-branded accessories contained in the original packaging (“Apple Product”) against defects in materials and workmanship when used normally in accordance with Apple's published guidelines for a period of ONE (1) YEAR from the date of original retail purchase by the end-user purchaser ("Warranty Period"). Apple’s published guidelines include but are not limited to information contained in technical specifications, user manuals and service communications.

Your iPhone's shattered glass was likely caused by a fall, not a material defect.

Apple One (1) Year Limited Warranty