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:

$x = -2$

This matches the answer you entered, so it seems like that part is correct. Double-check that no formatting issues or extra spaces may have caused the incorrect submission.

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.