find $g(x)$, where $g(x)$ is the translation 7 units down of $f(x)=x^{2}$. write your answer in the form…

find $g(x)$, where $g(x)$ is the translation 7 units down of $f(x)=x^{2}$. write your answer in the form $a(x - h)^{2}+k$, where $a$, $h$, and $k$ are integers. $g(x)=$

find $g(x)$, where $g(x)$ is the translation 7 units down of $f(x)=x^{2}$. write your answer in the form $a(x - h)^{2}+k$, where $a$, $h$, and $k$ are integers. $g(x)=$

Answer

Explanation:

Step1: Recall translation rule

For a vertical translation down by $n$ units of $y = f(x)$, the new function is $y=f(x)-n$.

Step2: Apply the rule to $f(x)=x^{2}$

Given $n = 7$ and $f(x)=x^{2}$, then $g(x)=x^{2}-7$. Writing it in the vertex - form $a(x - h)^{2}+k$, where $a = 1$, $h = 0$, and $k=-7$, we have $g(x)=1(x - 0)^{2}-7$.

Answer:

$1(x - 0)^{2}-7$