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\ng(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\ng(x) =

Answer

Explanation:

Step1: Identify vertex of $g(x)$

The vertex of $g(x)$ is at $(0, 8)$.

Step2: Recall vertex form formula

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

Step3: Substitute vertex values

Substitute $h=0$, $k=8$, and $a=1$ (since the parabola has the same width as $f(x)=x^2$): $g(x)=1(x-0)^2+8$

Step4: Simplify the expression

Simplify the terms to get the final function: $g(x)=x^2+8$

Answer:

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