Which of the following functions has a graph with a vertex that is a translation 5 units horizontally to the right of the vertex of the graph of f (x) = (x + 2) 2 + 2? Answer choices

A. g (x) = - (x - 3) 2 + 2

B. g (x) = (x + 7) 2 + 2

C. g (x) = (x + 5) 2 + 2

D. g (x) = - (x + 2) 2 + 5

g (x) = (x - 3) ^2 + 2

Step-by-step explanation:

f (x) = (x + 2) ^2 + 2

We want to shift this 5 units to the right

The parabola is written in the form

y = a (x-h) ^2 + k where (h, k) is the vertex

The vertex is at (-2, 2)

We want to shift it 5 units to the right

-2+5 = 3

g (x) = (x - 3) ^2 + 2