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

Explanation:

Step1: Identify vertex form

The function $f(x)=(x-5)^2+3$ uses the vertex form of a parabola: $f(x)=(x-h)^2+k$, where $(h,k)$ is the vertex.

Step2: Locate the vertex

For $f(x)=(x-5)^2+3$, $h=5$ and $k=3$, so the vertex is $(5, 3)$.

Step3: Match vertex to graph

Compare the vertex $(5,3)$ to the given graphs:

• First graph: Vertex at $(-5, -3)$
• Second graph: Vertex at $(-4, 3)$
• Third graph: Vertex at $(5, 3)$

Answer:

The third graph (rightmost one with vertex at (5, 3))