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Determine the domain and range of the graph.

The graph provided shows a downward-opening parabola. Let's determine its domain and range:

### Domain:
- The domain of a function is the set of all possible \( x \)-values that the function can take.
- From the graph, it appears that the parabola is defined for all \( x \)-values within the interval where the curve exists.
- The parabola starts at \( x = -2 \) and ends at \( x = 2 \).

Therefore, the domain is:
\[
\text{Domain} = [-2, 2]
\]

### Range:
- The range of a function is the set of all possible \( y \)-values that the function can take.
- From the graph, the maximum value of \( y \) is \( y = 4 \), which occurs at the vertex of the parabola.
- The minimum value of \( y \) on the graph is \( y = 0 \), as this is where the endpoints of the parabola lie on the x-axis.

Therefore, the range is:
\[
\text{Range} = [0, 4]
\]

Would you like more details on this explanation or have any further questions? Here are some related questions to consider:

1. How do you find the vertex of a parabola?
2. What are the properties of a parabola?
3. How do you determine if a parabola opens upwards or downwards?
4. Can the domain of a parabola ever be all real numbers?
5. What is the general form of a quadratic equation representing a parabola?

**Tip:** Remember that the domain of a function is all the possible input values (usually \( x \)-values), and the range is all possible output values (usually \( y \)-values).

Learn how to determine the domain and range of a downward-opening parabola with a detailed explanation. Understand the concepts of domain and range in functions, specifically quadratic functions. Suitable for high school students studying functions and quadratic equations.

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