find g(x), where g(x) is the reflection across the x - axis of f(x)=x². write your answer in the form a(x…

find g(x), where g(x) is the reflection across the x - axis of f(x)=x². 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)=x². 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 $g(x)=-f(x)$. Given $f(x)=x^{2}$, then $g(x)=-x^{2}$.

Step2: Rewrite in vertex - form

The vertex - form of a quadratic function is $a(x - h)^{2}+k$. For $g(x)=-x^{2}$, we can write it as $g(x)=-1(x - 0)^{2}+0$, where $a=-1$, $h = 0$, and $k = 0$.

Answer:

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