Certainly! Let's start by understanding the basic concept of shifting a function horizontally.
1. Quadratic Parent Function: The given parent function is [tex]\( F(x) = x^2 \)[/tex].
2. Horizontal Shifts: When we shift a function horizontally, we adjust the variable [tex]\( x \)[/tex] by adding or subtracting a constant.
3. Right Shift: If we shift the function to the right by [tex]\( n \)[/tex] units, we replace [tex]\( x \)[/tex] with [tex]\( (x - n) \)[/tex]. This is because to achieve the desired shift, [tex]\( x \)[/tex] has to reach the previous value earlier by [tex]\( n \)[/tex] units.
4. 12 Units Shift to the Right: In this case, we need to shift [tex]\( F(x) \)[/tex] 12 units to the right. Hence, we replace [tex]\( x \)[/tex] with [tex]\( (x - 12) \)[/tex].
5. New Function: Substituting [tex]\( x - 12 \)[/tex] into the parent function, we get the new function:
[tex]\[
G(x) = (x - 12)^2
\][/tex]
Thus, the equation of the new function after shifting [tex]\( F(x) = x^2 \)[/tex] to the right by 12 units is:
[tex]\[
G(x) = (x - 12)^2
\][/tex]
From the given options, the correct answer is:
A. [tex]\( G(x) = (x - 12)^2 \)[/tex]
So, the correct choice is option A.
