Final answer:
The vertex of the parabola represented by the given equation is (-3, 3), after rearranging it into vertex form. However, this result does not match any of the answer choices, indicating there might be a typo.
Step-by-step explanation:
To find the vertex of the graph of the given quadratic equation y + 2x + 3 = -(x + 2)^2 + 1, we first need to rewrite it in vertex form, which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
Let's rearrange the given equation:
y = -(x + 2)^2 + 1 - 2x - 3
y = -x^2 - 4x - 4 + 1 - 2x - 3
The equation simplifies to:
y = -x^2 - 6x - 6
Now, to find the vertex, we can complete the square or identify h and k from the equation y = a(x - h)^2 + k. The vertex form of this parabola is:
y = -(x + 3)^2 + 3
Here, a = -1, h = -3, and k = 3. Therefore, the vertex of the parabola is at (-3, 3).
Looking at the answer choices, the correct one is C) (-2, -3), but there seems to be a discrepancy as our calculation gives us (-3, 3). It is possible there might be a typo either in the question or the answer choices provided. Due to the calculated result not matching any of the proposed answers, please review the provided options for accuracy.