Shifting functions

Question

F(x)=x(squared) find the formula of the function g. It shifts right 2 and up 2

Answer 1

You move right by replacing x with x-2. You move up 2 by adding 2 to the function value. Thus,

f(x) = (x-2)² + 2 = x² -4x + 4 + 2 = x² -4x + 6

Answer 2

Eric,

Assuming it actually shifts right 3 and up 2 as in your Comment,

x → x - 3

f(x) → f(x) + 2

Combine these 2 shifts and get

x² → (x - 3)² + 2

The shifted function is

g(x) = (x - 3)² + 2 = (x² - 6x + 9) + 2 = x² - 6x + 11

g(x) = x² - 6x + 11

For the question as worded in your Comment, this is the correct shifted function.