precal

Patsy the parabola has an equation of y= x^2+2x+1. Every third friday of a month, Patsy opens downwards instead of upwards. On even dates, she translates two units the left. On odd dates, she translates 2 units to the right. She always reverts back to her original location at the end of the day. If the even date happens to fall on a Friday, she moves right instead of left. If the odd date happens to fall on a Monday, she moves left instead of right. What is the equation of Patsy on December 16th, 2016?