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

Explanation:

Step1: Identify the vertex - form of a parabola

The vertex - form of a parabola is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex of the parabola. For the function $f(x)=(x + 2)^2-3$, we have $a = 1$, $h=-2$, and $k=-3$.

Step2: Analyze the properties of the parabola

Since $a = 1>0$, the parabola opens upwards. The vertex of the parabola is at the point $(-2,-3)$.

Step3: Check the graphs for the vertex

We look for a graph of a parabola that opens upwards and has its vertex at the point $(-2,-3)$.

Answer:

The graph with a parabola opening upwards and vertex at $(-2,-3)$ (you would need to visually inspect the given graphs to pick the correct one based on the vertex and the upward - opening nature).