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.

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.

Answer

Explanation:

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

The vertex form of a parabola is ( a(x - h)^2 + k ), where ((h, k)) is the vertex. For ( f(x)=x^2 ), the vertex is ((0, 0)). From the graph of ( g(x) ), the vertex 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 ) (no vertical stretch or compression, just a horizontal translation), the value of ( a ) remains ( 1 ) (same as in ( f(x)=x^2 )).

Step3: Write the function rule for ( g(x) )

Substitute ( a = 1 ), ( h = -8 ), and ( k = 0 ) into the vertex form ( a(x - h)^2 + k ). We get ( g(x)=1(x - (-8))^2 + 0=(x + 8)^2 ).

Answer:

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