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Consider the following graph.

Step 2 of 2 :  

Determine the domain and range of the graph. Express your answer in interval notation.

To determine the **domain** and **range** of the graph, let's analyze the given parabola visually.

### Domain:
The domain represents all the possible values of \( x \) for which the function is defined.

- The graph extends horizontally from \( x = -5 \) to \( x = 5 \).
- Therefore, the domain is the closed interval \([-5, 5]\).

### Range:
The range represents all possible values of \( y \) that the graph takes.

- The graph reaches its lowest point at \( y = 0 \) (the vertex) and its highest point is at \( y = 10 \) (the top of the parabola).
- Therefore, the range is the closed interval \([0, 10]\).

### Final answer:
- **Domain**: \([-5, 5]\)
- **Range**: \([0, 10]\)

Would you like further details on how this is derived, or any questions about intervals?

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Here are five related questions to deepen your understanding:
1. What are the conditions that define a parabola's domain and range?
2. How do you determine the vertex of a parabola from its graph?
3. What happens to the domain and range if the parabola opens downwards instead?
4. How would the domain and range change if the graph were a different shape, like a circle?
5. Can you describe the difference between open and closed intervals in interval notation?

### Tip:
When analyzing graphs, always identify key points like the vertex and the intercepts to determine the domain and range easily.

Determine the domain and range of the graph. Express your answer in interval notation.

Learn how to determine the domain and range of a parabolic graph. This step-by-step guide explains how to analyze the graph visually and express the domain and range using interval notation. Suitable for students in Grades 8-10.

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