The given expression is \((x + 4)^2 + 1\), which represents a quadratic function in the form \(y = (x + 4)^2 + 1\).

To find the axis of symmetry for this quadratic function, we need to use the standard form of a quadratic function, which is:

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

Here:
- \(h\) represents the x-coordinate of the vertex.
- The axis of symmetry is given by the vertical line \(x = h\).

In the given equation \((x + 4)^2 + 1\), we can rewrite it as:

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

Thus, \(h = -4\). Therefore, the axis of symmetry is:

\[
x = -4
\]

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the vertex of the quadratic function \((x + 4)^2 + 1\)?
2. How do you determine if a quadratic function opens upwards or downwards?
3. Can you explain how the value of \(k\) in \(y = a(x - h)^2 + k\) affects the graph's position?
4. What would be the axis of symmetry for the function \((x - 2)^2 - 5\)?
5. How do you find the axis of symmetry if the quadratic function is not in vertex form?

**Tip:** The axis of symmetry always passes through the vertex of the parabola.

Discover how to find the axis of symmetry for the quadratic function (x+4)^2 + 1. This step-by-step explanation breaks down key algebraic concepts such as quadratic functions and the formula for axis of symmetry. Suitable for students in Grades 8-10.

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