since your mother and father are part owners they're are responsible for reporting their pro-rata share of the sale and do not qualify for the exclusion if they did not live in the house as their principal residence for 2 out of 5 years before sale. if you get all the proceeds, they have made a gift to you of their pro-rata share of the proceeds and if greater than the annual gift tax exclusion amount they are supposed to file a gift tax return though most likely they will owe no gift taxes.
reporting as far as your 1040 taxes: if a 1099-S is issued with your SSN, then you need to report it on your 1040 because the iRS will note it wasn't reported and since it doesn't know whether any amount is taxable. you will likely receive a notice.
i should mention that is it's your SSN, you'll need to report gross proceeds per the 1099 then show a reduction for the pro rata share belonging to your parents. also cost will need to be prorated