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 horizontal translation rule

For a parent function $f(x)$, $f(x-h)$ shifts the graph horizontally by $h$ units: right if $h>0$, left if $h<0$.

Step2: Match to given function

Compare $g(x)=(x-4)^2+2$ to $f(x-h)+k$. Here, $h=4$.

Answer:

4