If you shift the quadratic parent function, [tex]\( F(x) = x^2 \)[/tex], right 12 units, what is the equation of the new function?

A. [tex]\( G(x) = (x - 12)^2 \)[/tex]
B. [tex]\( G(x) = x^2 - 12 \)[/tex]
C. [tex]\( G(x) = x^2 + 12 \)[/tex]
D. [tex]\( G(x) = (x + 12)^2 \)[/tex]



Answer :

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.