Question

what is the equation of the translated function, $g(x)$, if $f(x)=x^2$?$\bigcirc$ $g(x)=(x-4)^2+6LXB0\bigcirc$ $g(x)=(x-6)^2-4$$\bigcirc$ $g(x)=(x+4)^2+6$

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 $(-4,6)$.

Step3: Use vertex form of parabola

Vertex form is $g(x)=(x-h)^2+k$, where $(h,k)$ is vertex. Substitute $h=-4$, $k=6$:
$g(x)=(x-(-4))^2+6=(x+4)^2+6$

Answer:

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