The image you provided contains a graph of a quadratic function, along with a question asking for specific values related to the function.

Graph Analysis and Interpretation:

1. Graph Details: The graph represents a parabola that opens downwards, indicating a negative leading coefficient in its equation.
2. Key Points:
   • Vertex: The highest point on the graph.
   • X-intercepts: Points where the graph crosses the x-axis.

Question Breakdown: The question appears to ask for the vertex and the x-intercepts of the quadratic function.

• Vertex: This is the point $(h, k)$ where the function reaches its maximum or minimum value. Based on the graph, this appears to be approximately at $(-0.5, 4)$.

• X-intercepts: These are the points where the graph crosses the x-axis. The graph seems to cross the x-axis at $x = -1$ and $x = 2$.

Solution:

1. Vertex: $(-0.5, 4)$
2. X-intercepts: $-1$ and $2$

Would you like more detailed steps on how to find these points, or do you have any other questions about the problem?

Relative Questions:

1. How do you calculate the vertex of a parabola algebraically?
2. What is the significance of the axis of symmetry in a quadratic function?
3. How can you determine if a quadratic function has real x-intercepts?
4. What role does the discriminant play in understanding the nature of the roots?
5. How do you derive the equation of a parabola from its graph?

Tip: When analyzing a quadratic function's graph, always identify the vertex and the x-intercepts first, as they provide critical information about the function's behavior.