The function g(x) is a translation of f(x) = (x + 3)2 – 10. The axis of symmetry of g(x) is 5 units to the right of f(x) . Which

Y=(x-h)^2+k
To shift the graph to the right by c units, the function becomes y=(x-h-c)^2+k
Indicating a move of 5 units to the right
g(x)=(x+3-5)^2-10
g(x)=(x-2)^2-10
first choice

The function provided is:

f(x)= (x+3)² - 10

We need to determine g(x), which is shifted 5 units to the right of f(x).

Firstly, by sketching the graph of f(x) using Desmos,[TAG_12]]

the shape of f(x) appears as a parabola with the vertex at (-3,-10).

The axis of symmetry is the line that bisects the parabola into two symmetrical halves.

Thus, the equation for g(x) can be expressed as g(x)= (x+3-5)² + K  →→→[∵ The axis of symmetry of g(x) moves 5 units to the right compared to f(x)]

g(x) = (x-2)² + K,  →→→→→  -∞≤ k≤∞

Setting K= -10 results in g(x)=(x-2)² -10, with the graphs of both f(x) and g(x) displayed below.

Option (A), g(x) = (x-2)² + K,  →→→→→  -∞≤ k≤∞ is the correct selection.