the graph shows ( g(x) ), which is a translation of ( f(x)=x^{2} ). write the function rule for ( g(x)…

the graph shows ( g(x) ), which is a translation of ( f(x)=x^{2} ). write the function rule for ( g(x) ).\nwrite your answer in the form ( a(x - h)^{2}+k ), where ( a ), ( h ), and ( k ) are integers or simplified fractions.\n( g(x)= )

the graph shows ( g(x) ), which is a translation of ( f(x)=x^{2} ). write the function rule for ( g(x) ).\nwrite your answer in the form ( a(x - h)^{2}+k ), where ( a ), ( h ), and ( k ) are integers or simplified fractions.\n( g(x)= )

Answer

Answer:

(g(x)=(x + 7)^2)

Explanation:

Step1: Recall the vertex form of a parabola

The vertex form of a parabola is (y = a(x - h)^2+k), where ((h,k)) is the vertex of the parabola.

Step2: Identify the vertex of (g(x))

For the function (f(x)=x^2), the vertex is ((0,0)). For the function (g(x)), from the graph, the vertex is ((- 7,0)). So (h=-7) and (k = 0).

Step3: Determine the value of (a)

Since there is no vertical stretch or compression (the parabola has the same "width" as (y=x^2)), (a = 1).

Step4: Substitute (a), (h), and (k) into the vertex form

Substitute (a = 1), (h=-7), and (k = 0) into (y=a(x - h)^2+k). We get (g(x)=1\times(x-(-7))^2+0=(x + 7)^2).