Question

what value represents the horizontal translation from the graph of the parent function ( f(x) = x^2 ) to the graph of the function ( g(x) = (x - 4)^2 + 2 )?
-4
-2
2
4

Explanation:

Step1: Recall vertex form rule

For $f(x)=(x-h)^2+k$, $h$ = horizontal shift.

Step2: Match to given function

$g(x)=(x-4)^2+2$, so $h=4$.

Step3: Interpret shift direction

Positive $h$ means shift right 4 units, so horizontal translation value is 4.

Answer:

D. 4