Question

The parabola y = x² is shifted up by 2 units and to the right by 3 units. What is the equation of the new parabola?

A. y = (x - 3)² + 2
B. y = (x + 3)² - 2
C. y = x² + 3x + 2
D. y = x² - 3x - 2

Answer 1

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.