The function you provided appears to have a duplication in its notation. Let's clean it up for clarity.

The correct function can be written as:

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

This represents a quadratic function. Let's break down the components:

1. **Vertex Form**: The function is already in a form similar to the vertex form of a quadratic function, which is:
   \[
   f(x) = a(x - h)^2 + k
   \]
   In this case:
   - \( a = 1 \)
   - \( h = -2 \) (since the function is \( (x + 2) \), \( h = -2 \))
   - \( k = -4 \)

2. **Vertex**: The vertex of the parabola described by this function is at \( (h, k) \), which is \((-2, -4)\).

3. **Direction**: Since \( a = 1 \) (which is positive), the parabola opens upwards.

4. **Axis of Symmetry**: The axis of symmetry is the vertical line that passes through the vertex, given by \( x = -2 \).

5. **Y-intercept**: To find the y-intercept, set \( x = 0 \):
   \[
   f(0) = (0 + 2)^2 - 4 = 4 - 4 = 0
   \]
   So, the y-intercept is at \( (0, 0) \).

Would you like more details on this function or have any questions?

Here are some related questions for further exploration:

1. How do you find the roots of the function \( f(x) = (x + 2)^2 - 4 \)?
2. What is the effect of changing the value of \( a \) on the graph of the quadratic function?
3. How would you complete the square for a more general quadratic function?
4. How does the discriminant help in determining the nature of the roots of a quadratic equation?
5. How would you graph \( f(x) = (x + 2)^2 - 4 \) by hand?

**Tip:** When dealing with quadratic functions, identifying the vertex early on can help you sketch the graph quickly and understand the function's behavior.

Explore the quadratic function f(x) = (x + 2)^2 - 4. Learn how to identify the vertex, axis of symmetry, and y-intercept, and understand the properties of parabolas. This guide is ideal for students in Grades 9-10.

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