Question

find g(x), where g(x) is the translation 3 units right of ( f(x) = x^2 ).
write your answer in the form ( a(x - h)^2 + k ), where a, h, and k are integers.
( g(x) = )
submit

Explanation:

Step1: Recall translation rules

For a function \( y = f(x) \), translating it \( h \) units to the right gives \( y = f(x - h) \). Here, \( f(x)=x^2 \) and we translate 3 units right.

Step2: Apply the translation

Substitute \( x - 3 \) into \( f(x) \). So \( g(x)=f(x - 3)=(x - 3)^2 \). In the form \( a(x - h)^2 + k \), \( a = 1 \), \( h = 3 \), \( k = 0 \).

Answer:

\( (x - 3)^2 \) (or \( 1(x - 3)^2+0 \))