1. **State the problem:** We analyze the parabola given by the equation $y = (x + 2)^2 + 3$. 2. **Identify the vertex:** The vertex form of a parabola is $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex. 3. **Rewrite the equation:** Here, $y = (x + 2)^2 + 3$ can be seen as $y = (x - (-2))^2 + 3$, so the vertex is at $(-2, 3)$. 4. **Axis of symmetry:** The axis of symmetry is the vertical line passing through the vertex, so it is $x = -2$. 5. **Direction of opening:** Since the coefficient of the squared term is positive ($a=1$), the parabola opens upwards. 6. **Domain:** The domain of any parabola is all real numbers, so $\text{Domain} = (-\infty, \infty)$. 7. **Range:** Because the parabola opens upwards and the vertex is the minimum point at $y=3$, the range is $y \geq 3$. **Final summary:** - Vertex: $(-2, 3)$ - Axis of symmetry: $x = -2$ - Opens: Upwards - Domain: $(-\infty, \infty)$ - Range: $[3, \infty)$