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When graphing the equation y = 2(x + 3)^2 + 1, what is the vertex?

  1. (3,1)

  2. (-3,1)

  3. (3,-1)

  4. (-3,-1)

The correct answer is: (-3,-1)

The vertex of a parabola is the highest or lowest point on the graph, also known as the maximum or minimum point. In the given equation, y = 2(x + 3)^2 + 1, the vertex form of a parabola is y = a(x - h)^2 + k, where (h,k) represents the vertex. Therefore, (h,k) = (-3,1), making (D) the correct answer. In option (A), the x-coordinate is correct, but the y-coordinate is incorrect. In options (B) and (C), both coordinates have been swapped from the correct answer.