https://file.aiquickdraw.com/mathbot/file/1726682799828azbc4spg.jpg

The given function is \( g(x) = (x + 3)^2 \). Let's work through the questions based on the transformations.

### a) Choose the correct parent function.
The function \( g(x) = (x + 3)^2 \) is derived from the parent function \( y = x^2 \), which is a standard quadratic function. So, the correct parent function is:
- **\( y = x^2 \)**

### b) Reflections
Since there is no negative sign outside the squared term, there is **no reflection** in this function.

### c) Stretches/Compressions
There is no coefficient stretching or compressing the function, so there is **no stretch or compression**.

### d) Vertical Shifts
There is no constant added or subtracted from the function after the squaring, so there is **no vertical shift**.

### e) Horizontal Shifts
The expression \( (x + 3) \) indicates a horizontal shift. The \( + 3 \) moves the graph **3 units to the left**.

### Summary of Transformations:
- **Parent function**: \( y = x^2 \)
- **Reflection**: None
- **Stretch/Compression**: None
- **Vertical Shift**: None
- **Horizontal Shift**: Left 3 units

Would you like further details on any of these steps? 

Here are 5 related questions to deepen understanding:
1. How do you determine the direction of a horizontal shift?
2. What happens to a graph when there is a reflection over the x-axis?
3. How does a coefficient outside of a squared term affect the graph?
4. How would the function change if it was \( g(x) = -(x + 3)^2 \)?
5. What are the effects of combining multiple transformations (e.g., reflection and shift)?

**Tip**: Always look for the signs inside the parentheses and their effects on horizontal shifts. A positive value shifts left, and a negative value shifts right.

Determine the parent function from which the graph of g(x) = (x + 3)^2 can be obtained. Identify the transformations that lead to the function's graph.

Learn how to transform the parent function y = x^2 to g(x) = (x + 3)^2. This covers horizontal shifts, reflections, and more. Suitable for students in Grades 9-11.

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