Question

find g(x), where g(x) is the translation 3 units down of f(x) = x². write your answer in the form a(x - h)² + k, where a, h, and k are integers. g(x) =

Explanation:

Step1: Recall vertical translation rule

For a function \( y = f(x) \), a vertical translation down by \( k \) units gives \( y = f(x)-k \).

Step2: Apply to given function

Given \( f(x)=x^{2} \), translating 3 units down: \( g(x)=x^{2}-3 \). Now, write in the form \( a(x - h)^{2}+k \). Here, \( a = 1 \), \( h = 0 \), \( k=- 3 \), so \( g(x)=1(x - 0)^{2}+(-3) \) or simply \( g(x)=(x - 0)^{2}-3 \) which is \( g(x)=x^{2}-3 \) in the required form.

Answer:

\( g(x) = 1(x - 0)^2 - 3 \) (or equivalently \( g(x) = x^2 - 3 \))