A parabola is represented by the equation...?

We can complete the square and get:
y = x² + 4x + 4 - 4
y = (x + 2)(x + 2) - 4
y = (x + 2)² - 4

That's in vertex form of a parabola:
y = a(x - h)² + k

In your case:
a = 1
h = -2
k = -4

Since 'a' is positive, you have an upward facing parabola where the vertex is therefore a minimum. The coordinate of the vertex is (-2, -4).

The line of symmetry goes through that vertex, so is x = -2.

Answer:
A. The parabola has a minimum at (-2, -4)
C. The parabola has an axis of symmetry of x = -2

The other statements don't apply to this parabola.

 A parabola is represented by the equation y = x^2 + 4x. 
 Which of the following is true about the parabola?
 A. The parabola has a minimum at (-2, -4). ✔
 B. The parabola has an axis of symmetry of x = 2.
 C. The parabola has an axis of symmetry at x = -2. ✔
 D.  The parabola has a maximum at (2, 4).