https://file.aiquickdraw.com/mathbot/file/1729188278288w9mt6z4q.jpg

The image shows the graph of a quadratic function, which forms a parabolic curve. To answer the question about the domain and range using interval notation, let’s analyze the graph step by step.

### Domain:
The domain refers to the set of all possible \( x \)-values (inputs) for the function. The graph extends horizontally from \( x = -5 \) to \( x = 5 \), meaning the function exists within these boundaries on the x-axis. Therefore, the domain in interval notation is:

\[
\boxed{[-5, 5]}
\]

### Range:
The range refers to the set of all possible \( y \)-values (outputs) for the function. From the graph, the highest point on the parabola occurs at \( y = 4 \) (the vertex), and the graph extends downward to the lowest point, which is at \( y = -4 \). Thus, the range in interval notation is:

\[
\boxed{[-4, 4]}
\]

Let me know if you'd like further details or have any questions.

Here are 5 related questions for further exploration:
1. How do you find the vertex of a parabola algebraically?
2. Can you determine the equation of the function based on the graph?
3. How would the domain and range change if the graph were shifted horizontally or vertically?
4. What would the interval notation look like if the graph extended beyond \( x = 5 \) or \( y = 4 \)?
5. How can you determine whether the parabola opens upwards or downwards from the equation?

**Tip**: In a parabola \( y = ax^2 + bx + c \), the sign of \( a \) determines the direction the parabola opens: if \( a > 0 \), it opens upwards, and if \( a < 0 \), it opens downwards.

Write the domain and range of the function shown in the graph using interval notation.

Learn how to determine the domain and range of a quadratic function from its graph. This example shows a parabolic curve with a domain of [-5, 5] and a range of [-4, 4], perfect for students in Grades 8-10.

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