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 transformation is $y=-f(x)$. Given $f(x)=x^{2}$, for the reflection $g(x)=-f(x)$.

Step2: Write in vertex - form

The vertex - form of a quadratic function is $a(x - h)^{2}+k$. For $y = x^{2}$, the vertex is $(0,0)$ i.e., $h = 0,k = 0$ and $a = 1$. After reflection across the $x -$axis, $a=-1,h = 0,k = 0$. So $g(x)=-1(x - 0)^{2}+0$.

Answer:

$g(x)=-(x - 0)^{2}+0$ or simply $g(x)=-x^{2}$