Day 2 investigations during an IVF cycle include a baseline ultrasound, antral follicle count, and measurements of estradiol, follicle stimulating hormone, luteinizing hormone, and progesterone levels. These tests help predict ovarian response by evaluating ovarian reserve function and developing an individualized ovarian hyperstimulation protocol. The tests provide information about follicle number and size, endometrial thickness, and hormone levels to classify ovaries and anticipate response to stimulation.