Answer:
4
Step-by-step explanation:
We are given that parent function
[tex]f(x)=x^2[/tex]
After translation of parent function
[tex]g(x)=(x-4)^2+2[/tex]
We have to find the value of horizontal translation from parent function to the function g(x).
General equation of parabola along y- axis
[tex]y=(x-h)^2+k[/tex]
The vertex of function is at (h,k).
The given function is an equation of parabola along y-a xis.
By comparing given function with general equation of parabola then
The vertex of function f(x) is at (0,0).
The vertex of function g(x) is at (4,2).
Therefore, h of f(x) is shift towards right and then we get h of g(x) =4
Hence, the value 4 represents the horizontal transformation from the graph of the parent function f(x) to the graph of the function g(x).
