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

the graph shows g(x), which is a translation of f(x)=x². write the function rule for g(x). write your answer in the form a(x - h)² + k, where a, h, and k are integers or simplified fractions. g(x) =

the graph shows g(x), which is a translation of f(x)=x². write the function rule for g(x). write your answer in the form a(x - h)² + k, where a, h, and k are integers or simplified fractions. g(x) =

Answer

Explanation:

Step1: Identify vertex form parameters

The vertex - form of a quadratic function is $y = a(x - h)^2 + k$, where $(h,k)$ is the vertex of the parabola. For the function $f(x)=x^{2}$, its vertex is $(0,0)$. For the function $g(x)$, the vertex is $(2,0)$, so $h = 2$ and $k = 0$.

Step2: Determine the value of a

Since the parabola $g(x)$ has the same shape as $f(x)=x^{2}$, the value of $a$ is the same as in $f(x)$. For $f(x)=x^{2}$, $a = 1$. And the transformation from $f(x)$ to $g(x)$ is a horizontal translation, which does not change the value of $a$. So $a=1$.

Answer:

$g(x)=(x - 2)^{2}$