Which is the graph of f(x) = -(x + 3)(x + 1)?

Step-by-step explanation:

Setting f(x) = -(x + 3)(x + 1) = 0 leads to identifying two roots/solutions of this equation:  x = -3 and x = -1.  The axis of symmetry is a vertical line halfway between these two roots:  x = -2.  This x = -2 is also the x-coordinate of the vertex.  Evaluating f(x) = -(x + 3)(x + 1) at x = -2 gives us the y-coordinate of the vertex:  y = -(-2 + 3)(-2 + 1) = -(1)(-1) = 1.

In summary, the vertex is at (-2, 1) and the two x-intercepts are (-3, 0) and (-1, 0).  The y-intercept is found by  setting x = 0 and finding y:  

f(0) = -(0 + 3)(0 + 1) = -3, or (0, -3)

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