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To solve the given problem, we need to identify the axis of symmetry for the quadratic function:

\[
f(x) = 4(x + 2)^2 - 1
\]

This is a standard quadratic function in vertex form: 

\[
f(x) = a(x - h)^2 + k
\]

In this form, the axis of symmetry is the vertical line \( x = h \), where \( h \) is the x-coordinate of the vertex.

For the function \( f(x) = 4(x + 2)^2 - 1 \), you can see that \( h = -2 \) because \( (x + 2) \) indicates a shift 2 units to the left (the vertex form has \( (x - h) \), so \( (x + 2) \) means \( h = -2 \)).

Therefore, the axis of symmetry is:

\[
x = -2
\]

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Would you like further clarification or details on this?

Here are five related questions to deepen your understanding:
1. How do you find the vertex of a quadratic function?
2. What does the coefficient \( a \) in a quadratic function tell us about its graph?
3. How would the graph of \( f(x) = 4(x + 2)^2 - 1 \) compare to \( f(x) = (x + 2)^2 - 1 \)?
4. How can you derive the axis of symmetry from a standard form quadratic equation \( ax^2 + bx + c \)?
5. What is the significance of the constant term in a quadratic function's vertex form?

**Tip:** The vertex form of a quadratic function is especially useful for identifying the vertex and axis of symmetry directly, without the need for further calculations.

Identify the axis of symmetry: f(x) = 4(x + 2)^2 - 1

Understand how to find the axis of symmetry for the quadratic function f(x) = 4(x + 2)^2 - 1. This detailed solution covers the vertex form and explains how to identify the axis of symmetry based on the equation. Suitable for high school students in Grades 9-11.

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