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

Explanation:

Step1: Recall the vertex form of a parabola

The vertex form of a parabola is (g(x)=a(x - h)^{2}+k), where ((h,k)) is the vertex of the parabola. For the parent function (f(x)=x^{2}), (a = 1), (h=0), (k = 0).

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

From the graph, the vertex of (g(x)) is ((- 3,0)). So (h=-3) and (k = 0).

Step3: Substitute (h) and (k) into the vertex form

Substitute (h=-3) and (k = 0) into (g(x)=a(x - h)^{2}+k). Since the parabola has the same shape as (f(x)=x^{2}) (no vertical stretch or compression, so (a = 1)). [g(x)=(x-(-3))^{2}+0] [g(x)=(x + 3)^{2}]

Answer:

(g(x)=(x + 3)^{2})