Question

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

Answer 1

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

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