find $g(x)$, where $g(x)$ is the reflection across the $x$-axis of $f(x)=x^{2}$. write your answer in the…

find $g(x)$, where $g(x)$ is the reflection across the $x$-axis 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 reflection across the $x$-axis 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 reflection rule

When a function $y = f(x)$ is reflected across the $x -$axis, the new function $g(x)=-f(x)$.

Step2: Substitute $f(x)$

Given $f(x)=x^{2}$, then $g(x)=-x^{2}$. In the vertex - form $a(x - h)^{2}+k$, for $g(x)=-x^{2}$, we have $a=-1$, $h = 0$, and $k = 0$. So $g(x)=-1(x - 0)^{2}+0$.

Answer:

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