Final answer:
The equation of the new parabola is y = (x - 3)² + 2.
Step-by-step explanation:
The equation of the original parabola is y = x². To shift the parabola up by 2 units, we add 2 to the equation, resulting in y = x² + 2. To shift the parabola to the right by 3 units, we replace x with (x - 3), giving us y = (x - 3)² + 2. Therefore, the equation of the new parabola is y = (x - 3)² + 2, so the correct answer is A.