https://file.aiquickdraw.com/mathbot/file/17265766483033uaxy7yy.jpg

The graph you provided represents a quadratic function, which typically has a parabolic shape. Based on the graph:

### Domain:
The domain of a quadratic function, like the one shown in the image, is **all real numbers** because the parabola extends infinitely to the left and right on the x-axis. In mathematical notation:
\[
\text{Domain} = (-\infty, \infty)
\]

### Range:
The range of the function depends on the minimum or maximum value of the parabola. Since this parabola opens upwards, its lowest point (vertex) appears to be around \(y = 6\), and the parabola continues upwards from there. Therefore, the range is all values greater than or equal to 6. In mathematical notation:
\[
\text{Range} = [6, \infty)
\]

Let me know if you need further details!

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Here are 5 related questions for deeper understanding:
1. How can we find the exact vertex of a parabola algebraically?
2. What is the general form of a quadratic function, and how does it help in determining the direction of the parabola?
3. How would the domain and range change if the parabola opened downwards?
4. What is the significance of the axis of symmetry in determining the properties of a quadratic graph?
5. How can you calculate the x-intercepts of a parabola using the quadratic formula?

**Tip**: Always check the vertex of a parabola to determine the range, especially if the graph is not perfectly aligned to the grid.

Learn how to determine the domain and range of a quadratic function from its graph. In this case, the domain is all real numbers, and the range starts from the vertex value upwards. This is an essential concept in algebra and functions, suitable for high school students.

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