Apple`s warranty is a limited coverage one,
not a full replacement warranty.
it will not cover cracked or shattered screens that were caused by dropping it on the floor.
Apple care only pays for manufacturer`s defects that were caused during the making of the iPhone,
not damage that was caused by user misuse or mistakes.
you`re out of luck and will have to pay for the repairs out of your own pocket.
By the way,
the cost to replace the LCD touchscreen is NOT CHEAP!
Apples charges 200 to fix a broken screen.