the graph of $g(x)$ is a translation of the function $f(x)=x^{2}$. the vertex of $g(x)$ is located 5 units…

the graph of $g(x)$ is a translation of the function $f(x)=x^{2}$. the vertex of $g(x)$ is located 5 units above and 7 units to the right of the vertex of $f(x)$. which equation represents $g(x)$?\n$g(x)=(x + 7)^{2}+5$\n$g(x)=(x - 7)^{2}+5$\n$g(x)=(x + 5)^{2}+7$\n$g(x)=(x - 5)^{2}+7$

the graph of $g(x)$ is a translation of the function $f(x)=x^{2}$. the vertex of $g(x)$ is located 5 units above and 7 units to the right of the vertex of $f(x)$. which equation represents $g(x)$?\n$g(x)=(x + 7)^{2}+5$\n$g(x)=(x - 7)^{2}+5$\n$g(x)=(x + 5)^{2}+7$\n$g(x)=(x - 5)^{2}+7$

Answer

Explanation:

Step1: Recall vertex - form of a quadratic function

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

Step2: Determine the new vertex

The vertex of $g(x)$ is located 5 units above and 7 units to the right of the vertex $(0,0)$ of $f(x)$. So the vertex of $g(x)$ is $(7,5)$.

Step3: Write the equation of $g(x)$

Substitute $h = 7$ and $k = 5$ into the vertex - form $y=a(x - h)^2 + k$. Since $a = 1$ (the coefficient of $x^{2}$ in $f(x)=x^{2}$ and the shape of the parabola is not changed by translation), the equation of $g(x)$ is $g(x)=(x - 7)^2+5$.

Answer:

$g(x)=(x - 7)^2 + 5$