The problem presented involves identifying key properties of a parabola from its graph. Let's break down the elements visible in the image:

1. Vertex: The vertex of a parabola is the highest or lowest point on the graph. Based on the graph, the vertex appears to be at the coordinates (-2, 4).

2. Axis of Symmetry: The axis of symmetry of a parabola is a vertical line that passes through the vertex. From the graph, this line is $x = -2$, since the vertex lies on this line.

3. Direction of Opening: The parabola in the graph opens downwards because the arms of the parabola are pointing downwards. This can be inferred from the fact that the vertex is a maximum point.

Here is a summary of the properties:

• Vertex: $(-2, 4)$
• Axis of Symmetry: $x = -2$
• Parabola Opens: Downwards

Would you like more details on how to derive these properties from the graph, or do you have any specific questions?

Here are five questions you could explore next:

1. How can the vertex form of a quadratic equation help in identifying the vertex?
2. What is the significance of the axis of symmetry in a parabola?
3. How do you determine if a parabola opens upwards or downwards from its equation?
4. How would you find the focus of the parabola given its vertex and direction of opening?
5. How does the value of the coefficient $a$ in the equation $y = ax^2 + bx + c$ affect the width and direction of the parabola?

Tip: The vertex form of a parabola is written as $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex, and $a$ determines if the parabola opens upwards ($a > 0$) or downwards ($a < 0$).