what is the equation of the translated function, g(x), if f(x)=x²?\n○ g(x)=(x - 4)²+6\n○ g(x)=(x + 6)²-4\n○…

Answer:

D. $g(x)=(x + 4)^2+6$

Explanation:

Step1: Recall translation rules

For $y = f(x - h)^2 + k$, $h$ is horizontal shift and $k$ is vertical shift.

Step2: Analyze horizontal shift

The vertex of $f(x)=x^2$ is $(0,0)$. The vertex of $g(x)$ is $(- 4,6)$. To move from $x = 0$ to $x=-4$, we use $x+4$ (left - shift by 4 units as $h=-4$).

Step3: Analyze vertical shift

To move from $y = 0$ to $y = 6$, we add 6 to the function. So $g(x)=(x + 4)^2+6$.