what value represents the horizontal translation from the graph of the parent function f(x) = x² to the…

Explanation:

Step1: Recall function - translation rule

For a quadratic function of the form $y = a(x - h)^2 + k$, the graph of the parent - function $y = ax^2$ is translated $h$ units horizontally and $k$ units vertically.

Step2: Identify the value of $h$ in $g(x)$

Given $g(x)=(x - 4)^2+2$, comparing it with the vertex - form $y=a(x - h)^2 + k$, we have $h = 4$ and $k = 2$. The horizontal translation is determined by the value of $h$. A positive $h$ value means a right - hand translation and a negative $h$ value means a left - hand translation.

Answer:

D. 4