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

Explanation:

Step1: Identify vertex form

The function is in vertex form $f(x) = (x-h)^2 + k$, where $(h,k)$ is the vertex. For $f(x)=(x+2)^2-3$, rewrite as $f(x)=(x-(-2))^2 + (-3)$.

Step2: Find vertex coordinates

From the rewritten form, $h=-2$, $k=-3$. So the vertex is $(-2, -3)$.

Step3: Match vertex to graph

Check each graph:

• First graph: vertex at $(-2, -3)$
• Second graph: vertex at $(1, -3)$
• Third graph: vertex at $(1, 3)$

Answer:

The first graph (leftmost one, with vertex at $(-2, -3)$)