Question

which graph represents the function ( f(x) = (x - 5)^2 + 3 )?

Explanation:

Step1: Identify vertex form

The function is in vertex form $f(x) = (x-h)^2 + k$, where $(h,k)$ is the vertex.

Step2: Locate the vertex

For $f(x) = (x-5)^2 - 3$, $h=5$, $k=-3$. So vertex is $(5, -3)$.

Step3: Match vertex to graph

Check which graph has vertex at $(5, -3)$ (right 5 on x-axis, down 3 on y-axis). The top graph has its vertex at this point, while the bottom graph has a vertex left of the y-axis.

Answer:

The top graph (the first option with vertex at (5, -3)) represents the function $f(x)=(x-5)^2 - 3$.