Question

determining the appearance of a graph
which graph represents ( f(x) = (x + 2)^2 - 3 )?

Explanation:

Step1: Identify vertex form

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

Step2: Find vertex coordinates

For $f(x) = (x+2)^2 - 3$, rewrite it as $f(x) = (x-(-2))^2 + (-3)$. So $h=-2$, $k=-3$, vertex is $(-2, -3)$.

Step3: Match vertex to graph

Look for the parabola with vertex at $(-2, -3)$. The first graph has its lowest point at $(-2, -3)$.

Answer:

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