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To determine the domain and range of the quadratic function based on the graph provided:

1. **Domain**: The domain of a function represents all possible values of \(x\). From the graph, the curve extends from \(x = -2\) to \(x = 8\), so the domain is the interval \([-2, 8]\).

2. **Range**: The range represents all possible values of \(y\). The graph shows that the highest point (vertex) of the parabola is at \(y = 5\), and the parabola opens downward. The lowest value of \(y\) continues downward to negative infinity. Therefore, the range is \((-\infty, 5]\).

Thus, the correct answers are:
- **Domain**: \([-2, 8]\)
- **Range**: \((-\infty, 5]\)

Would you like further clarification on this or related concepts?

### Relative Questions:
1. How do you determine the vertex of a parabola from a quadratic function?
2. What happens to the domain and range when a parabola opens upward instead of downward?
3. How does the axis of symmetry of a parabola relate to its domain and range?
4. Can the domain of a quadratic function ever be limited in real-life situations?
5. How can you find the domain and range of a function algebraically without graphing it?

**Tip**: For a quadratic function, the domain is often all real numbers unless specified otherwise by constraints in a graph or context.

What is the domain and range of the following quadratic function?

Learn how to find the domain and range of a quadratic function by analyzing its graph. This example covers key algebraic concepts and graph interpretation skills. Suitable for students in Grades 9-10.

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