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.