the graph shows $g(x)$, which is a translation of $f(x) = x^2$. write the function rule for $g(x)$…

the graph shows $g(x)$, which is a translation of $f(x) = x^2$. write the function rule for $g(x)$. \n\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 $f(x) = x^2$. write the function rule for $g(x)$. \n\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 vertex of $f(x)$

The parent function $f(x)=x^2$ has vertex at $(0,0)$.

Step2: Identify vertex of $g(x)$

From the graph, $g(x)$ has vertex at $(0,10)$.

Step3: Substitute into vertex form

Vertex form is $g(x)=a(x-h)^2+k$, where $(h,k)$ is vertex. Here $a=1$ (no stretch/compression), $h=0$, $k=10$. <Expression> $g(x)=1(x-0)^2+10$ </Expression>

Step4: Simplify the function rule

Simplify the expression to get the final form. <Expression> $g(x)=x^2+10$ </Expression>

Answer:

$g(x)=x^2+10$