the function $g(x)$ is a translation of $f(x)=(x + 3)^2-10$. the axis of symmetry of $g(x)$ is 5 units to…

the function $g(x)$ is a translation of $f(x)=(x + 3)^2-10$. the axis of symmetry of $g(x)$ is 5 units to the right of $f(x)$. which function could be $g(x)$?\n$g(x)=(x - 2)^2 + k$\n$g(x)=(x + 8)^2 + k$\n$g(x)=(x - h)^2-5$\n$g(x)=(x - h)^2-15$

the function $g(x)$ is a translation of $f(x)=(x + 3)^2-10$. the axis of symmetry of $g(x)$ is 5 units to the right of $f(x)$. which function could be $g(x)$?\n$g(x)=(x - 2)^2 + k$\n$g(x)=(x + 8)^2 + k$\n$g(x)=(x - h)^2-5$\n$g(x)=(x - h)^2-15$

Answer

Explanation:

Step1: Find axis of symmetry of $f(x)$

For a quadratic function in vertex - form $y=a(x - h)^2 + k$, the axis of symmetry is $x = h$. For $f(x)=(x + 3)^2-10$, where $h=-3$, the axis of symmetry of $f(x)$ is $x=-3$.

Step2: Determine axis of symmetry of $g(x)$

The axis of symmetry of $g(x)$ is 5 units to the right of $f(x)$'s axis of symmetry. So, $x=-3 + 5=2$.

Step3: Identify the form of $g(x)$

For a quadratic function $g(x)=(x - m)^2 + n$, its axis of symmetry is $x = m$. Since the axis of symmetry of $g(x)$ is $x = 2$, the function $g(x)$ has the form $g(x)=(x - 2)^2 + k$.

Answer:

$g(x)=(x - 2)^2 + k$