Question

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

Explanation:

Step1: Identify vertex of $f(x)$

The vertex of $f(x)=x^2$ is $(0,0)$.

Step2: Identify vertex of $g(x)$

From the graph, the vertex of $g(x)$ is $(-4,6)$.

Step3: Use vertex form of parabola

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

Answer:

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