https://file.aiquickdraw.com/mathbot/file/1726350959542brjpfo3p.jpg

From the graph you provided, it appears to be a parabola that opens upwards. Let's identify the **domain** and **range** based on the features of the parabola.

### Domain:
The domain of a parabola like this is the set of all possible \(x\)-values for which the function is defined. Since the parabola extends infinitely in both directions along the \(x\)-axis, the domain is all real numbers.

**Domain:**
\[
(-\infty, \infty)
\]
or in interval notation, \(x \in \mathbb{R}\).

### Range:
The range of a function is the set of all possible \(y\)-values. In this graph, the parabola has its lowest point at \(y = 0\) and opens upwards. Thus, the \(y\)-values start from 0 and increase without bound.

**Range:**
\[
[0, \infty)
\]
or \(y \geq 0\).

Would you like more details on how to interpret this graph?

### Here are 5 related questions to deepen your understanding:
1. How do we determine the vertex of a parabola from its equation or graph?
2. What is the equation of this parabola based on the graph?
3. How do you find the axis of symmetry of a parabola?
4. How does the direction (upward or downward) of the parabola affect its range?
5. What are the properties of a quadratic function that describe its behavior?

### Tip:
When identifying the domain and range of a parabola, always consider whether it opens upwards or downwards, as this influences whether the range is limited from below or from above.

This tutorial explains how to find the domain and range of a parabola. By analyzing the graph of a quadratic function, you can determine that the domain includes all real numbers, while the range starts at 0 and extends to infinity.

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