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The problem describes a quadratic function with a maximum value of \(-3\) at \(x = 8\).

### Domain of a Quadratic Function:
The domain of any quadratic function is all real numbers since a parabola extends infinitely in both the positive and negative directions on the \(x\)-axis.

Therefore, the **domain** of the function is:
\[
(-\infty, \infty)
\]

Would you like to explore the range or any further details? 

Here are some related questions for further exploration:

1. What is the range of the given quadratic function?
2. How do you determine if a quadratic function opens upwards or downwards?
3. Can a quadratic function have more than one maximum or minimum point?
4. How does the vertex form of a quadratic function help in determining its properties?
5. What is the significance of the axis of symmetry in a quadratic function?

**Tip:** When dealing with quadratic functions, identifying the vertex can help quickly determine both the maximum or minimum value and the range.

Give the domain and range of the quadratic function whose graph is described. Maximum = -3 at x = 8.

Learn how to find the domain and range of a quadratic function with a given maximum value. This example describes a parabola with a maximum of -3 at x = 8, ideal for students in Grades 9-11 exploring quadratic functions.

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