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

find ( g(x) ), where ( g(x) ) is the reflection across the ( x )-axis of ( f(x)=x^{2} ).\nwrite your answer in the form ( a(x - h)^{2}+k ), where ( a ), ( h ), and ( k ) are integers.\n( g(x)= )

find ( g(x) ), where ( g(x) ) is the reflection across the ( x )-axis of ( f(x)=x^{2} ).\nwrite your answer in the form ( a(x - h)^{2}+k ), where ( a ), ( h ), and ( k ) are integers.\n( g(x)= )

Answer

Explanation:

Step1: Recall the 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}), then ( g(x)=-f(x) ).

Step2: Substitute ( f(x) ) into the reflection formula

Substitute ( f(x) = x^{2} ) into ( g(x)=-f(x) ). We get ( g(x)=-(x - 0)^{2}+0) (since ( f(x)=x^{2}=(x - 0)^{2}+0) in the vertex form ( a(x - h)^{2}+k)).

Answer:

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