To determine the domain of the curve shown in the graph, we need to analyze the range of x-values for which the function is defined.

### Analyzing the Curve:
The curve shown in the image is a parabola that opens upwards. Parabolas that open upwards or downwards typically have domains that extend infinitely in both the positive and negative directions along the x-axis.

### Domain of a Parabola:
For a parabola of the general form \( y = ax^2 + bx + c \), the domain is all real numbers, because there are no restrictions on the x-values that can be input into the equation.

### Conclusion:
The domain of the curve in the graph is:

\[
\text{Domain: } (-\infty, \infty)
\]

This means that the function is defined for all real values of \( x \).

### Would you like more details or have any questions?

### Related Questions:
1. How do you find the range of a parabola?
2. What happens to the domain if the parabola is part of a real-world scenario, like projectile motion?
3. Can the domain of a parabola ever be restricted? If so, how?
4. How would the domain change if there were asymptotes involved?
5. What is the domain of other types of functions, like square roots or logarithms?

### Tip:
When dealing with quadratic functions or parabolas, the domain is always all real numbers, unless there's a specific real-world context or a specific problem that limits the range of possible x-values.

Learn how to determine the domain of a parabola shown in a graph. Explore the mathematical analysis of quadratic functions and understand why the domain of a parabola is always all real numbers. Suitable for high school students.

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