Answer :
To determine the horizontal translation from the parent function \( f(x) = x^2 \) to the function \( g(x) = (x-4)^2 + 2 \), we need to analyze the form of the function \( g(x) \).
The function \( g(x) \) can be written as:
[tex]\[ g(x) = (x-h)^2 + k \][/tex]
where \( h \) represents the horizontal shift and \( k \) represents the vertical shift.
In the given function \( g(x) = (x-4)^2 + 2 \):
- The expression inside the parentheses, \( x-4 \), indicates a horizontal shift.
- The number subtracted inside the parentheses (in this case, 4) tells us the direction and magnitude of the horizontal translation.
Specifically, \( x-4 \) means that every \( x \)-value of the parent function \( f(x) \) is shifted to the right by 4 units.
So, the value representing the horizontal translation is:
[tex]\[ 4 \][/tex]
Therefore, the correct answer is:
[tex]\[ 4 \][/tex]
The function \( g(x) \) can be written as:
[tex]\[ g(x) = (x-h)^2 + k \][/tex]
where \( h \) represents the horizontal shift and \( k \) represents the vertical shift.
In the given function \( g(x) = (x-4)^2 + 2 \):
- The expression inside the parentheses, \( x-4 \), indicates a horizontal shift.
- The number subtracted inside the parentheses (in this case, 4) tells us the direction and magnitude of the horizontal translation.
Specifically, \( x-4 \) means that every \( x \)-value of the parent function \( f(x) \) is shifted to the right by 4 units.
So, the value representing the horizontal translation is:
[tex]\[ 4 \][/tex]
Therefore, the correct answer is:
[tex]\[ 4 \][/tex]
