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.