https://file.aiquickdraw.com/mathbot/file/1726707382357ygf4asx2.jpg

The graph provided shows a parabolic curve, and two points on the curve are highlighted: approximately (-2, 3) and (2, 3). Based on this, we can determine the **domain** and **range** of the function represented by the graph.

### Domain:
The domain refers to the set of all possible \( x \)-values that the function can take. From the graph, we can see that the curve continues indefinitely along the x-axis. Thus, the domain is:

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

### Range:
The range refers to the set of all possible \( y \)-values that the function can take. The graph shows that the lowest point on the curve is at \( y = -1 \), and the curve extends upwards without bound. Therefore, the range is:

\[
\text{Range: } [-1, \infty)
\]

Would you like further details or have any questions?

Here are 5 questions that could help deepen your understanding:
1. How can we express the equation of a parabola given its vertex and points?
2. What is the vertex form of a quadratic function?
3. How do the points \((-2, 3)\) and \((2, 3)\) influence the symmetry of the graph?
4. How can we determine the axis of symmetry of a parabola?
5. How would the domain and range change if the parabola opened downward?

**Tip:** The vertex of a parabola is the point where it changes direction, and it plays a key role in determining the range of the function.

Explore the domain and range of a quadratic function based on a parabolic graph. Understand key algebraic concepts like quadratic functions, symmetry, and the significance of the vertex in determining the range. Suitable for students in Grades 8-10.

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