https://file.aiquickdraw.com/mathbot/file/1726024664567i0vypuox.jpg

The graph shows a quadratic function with a vertex at \( (-3, 3) \). Since the parabola opens upwards (it has a "U" shape), we can determine the following:

### Domain:
The domain of a quadratic function is always all real numbers because a parabola extends infinitely to the left and right. Therefore, the domain in interval notation is:
\[
\boxed{(-\infty, \infty)}
\]

### Range:
The range of the function is determined by the lowest point on the graph, which is the y-coordinate of the vertex. Since the parabola opens upwards, the minimum value of \( y \) is 3 (the y-coordinate of the vertex), and the function takes on all values greater than or equal to this point. Therefore, the range in interval notation is:
\[
\boxed{[3, \infty)}
\]

Would you like further details on how to derive this? 

Here are five related questions for further practice:
1. What is the axis of symmetry of the parabola?
2. How do you find the vertex form of a quadratic function given the vertex?
3. What is the effect of changing the vertex on the graph of a parabola?
4. How would the domain and range change if the parabola opened downward instead of upward?
5. Can you determine the equation of the parabola from the given graph?

**Tip:** The range of a parabola is always influenced by whether it opens upwards or downwards. The vertex will either be a minimum (for upward-opening) or maximum (for downward-opening).

The graph of a quadratic function with vertex (-3, 3) is shown in the figure below. Find the domain and the range. Write the domain and range using interval notation.

Learn how to determine the domain and range of a quadratic function with vertex (-3, 3). This guide covers quadratic function properties, domain, range, and how to express them using interval notation. Ideal for students in Grades 8-10.

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