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.

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.

Answer

Explanation:

Step1: Identify vertex

The vertex - form of a parabola is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex of the parabola. From the graph, the vertex of the parabola $g(x)$ is $(0,0)$, so $h = 0$ and $k = 0$.

Step2: Find the value of a

We know that the parent - function is $f(x)=x^2$. Let's take a non - vertex point on the graph of $g(x)$, say $(2,1)$. Substitute $x = 2$, $y = 1$, $h = 0$, and $k = 0$ into the equation $y=a(x - h)^2+k$. We get $1=a(2 - 0)^2+0$, which simplifies to $1 = 4a$. Solving for $a$, we divide both sides by 4, so $a=\frac{1}{4}$.

Answer:

$g(x)=\frac{1}{4}x^{2}$