Answer:
The value of horizontal shift is [tex]-4[/tex] that means graph of parent function is shifted to right by 4 units.
Step-by-step explanation:
We have been given a parent function [tex]f(x)=x^2[/tex] and another function [tex]g(x)=(x-4)^2+2[/tex]. We are asked to determine the horizontal translation from the graph of the parent function to the graph of the function g(x).
Let us recall translation rules.
Horizontal translation:
[tex]f(x)\rightarrow f(x-a)=\text{Graph shifted to the right by 'a' units}[/tex]
[tex]f(x)\rightarrow f(x+a)=\text{Graph shifted to the left by 'a' units}[/tex]
Vertical translation:
[tex]f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by 'a' units}[/tex]
[tex]f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by 'a' units}[/tex]
Upon looking at our both functions, we can see that parent function is shifted to right by 4 units and upwards by 2 units to get the the function g(x).
Therefore, the value of horizontal translation is [tex]-4[/tex], which indicates the graph is shifted to right by 4 units.
