the graph shows g(x), which is a translation of f(x) = x². write the function rule for g(x).\nwrite your…

the graph shows g(x), which is a translation of f(x) = x². 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) = x². 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

Explanation:

Step1: Identify the vertex of ( g(x) )

The vertex form of a quadratic function is ( a(x - h)^2 + k ), where ((h, k)) is the vertex. From the graph, the vertex of ( g(x) ) is at ((8, 0)), so ( h = 8 ) and ( k = 0 ).

Step2: Determine the value of ( a )

Since ( g(x) ) is a translation of ( f(x)=x^2 ) (which has ( a = 1 )) and there's no vertical stretch or compression (the shape is the same as ( f(x) )), ( a = 1 ).

Step3: Write the function rule

Substitute ( a = 1 ), ( h = 8 ), and ( k = 0 ) into the vertex form: ( g(x)=1(x - 8)^2+0 ), which simplifies to ( g(x)=(x - 8)^2 ).

Answer:

( g(x)=(x - 8)^2 )