y=(×+2)^2-3 find the domain of the function

The function given is \( y = (x + 2)^2 - 3 \).

### Finding the Domain:
The domain of a function is the set of all possible input values (usually \( x \)-values) for which the function is defined.

For the function \( y = (x + 2)^2 - 3 \), there are no restrictions on \( x \). This is because:
- The function involves a squared term, \( (x + 2)^2 \), which is defined for all real numbers.
- Subtracting 3 does not impose any additional restrictions.

Thus, the domain of the function is **all real numbers**.

### Domain in Set Notation:
\[ \text{Domain: } x \in (-\infty, \infty) \]

Would you like more details or have any questions?

Here are some related questions:
1. What is the range of the function \( y = (x + 2)^2 - 3 \)?
2. How do you find the vertex of the parabola described by this function?
3. What is the axis of symmetry for the function \( y = (x + 2)^2 - 3 \)?
4. How does the graph of \( y = (x + 2)^2 - 3 \) compare to the graph of \( y = x^2 \)?
5. How can you determine the intercepts of the function \( y = (x + 2)^2 - 3 \)?

**Tip:** The domain of a polynomial function is always all real numbers unless the function includes a fraction or a square root.

Learn how to find the domain of the function (x + 2)^2 - 3 with a detailed step-by-step solution. Understand why the domain includes all real numbers and how to represent it in set notation. Suitable for high school students.

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