what is the equation of the translated function, g(x), if f(x)=x²?\n○ g(x)=(x + 5)²+2\n○ g(x)=(x + 2)²+5\n○…

Answer:

D. $g(x)=(x - 5)^2+2$

Explanation:

Step1: Recall translation rules

For a function $y = f(x)$, a horizontal translation $h$ units to the right and a vertical translation $k$ units up gives $y=f(x - h)+k$.

Step2: Analyze the graph

The graph of $f(x)=x^{2}$ (vertex at $(0,0)$) is translated 5 units to the right and 2 units up. Here $h = 5$ and $k=2$.

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

Substitute $h = 5$ and $k = 2$ into $y=f(x - h)+k$. Since $f(x)=x^{2}$, we get $g(x)=(x - 5)^2+2$.