Compare the graph of g(x) = -1/2x^2 - 2 with the graph of f(x) = x^2.
The graph of g(x) is narrower than the graph of f(x). The graph of g(x) opens downward, and the graph of f(x) opens upward. The axis of symmetry is the same. The vertex of f(x) is (0, 0). The vertex of g(x) is translated down 2 units to (0, –2).
The graph of g(x) is wider than the graph of f(x). The graph of g(x) opens downward, and the graph of f(x) opens upward. The axis of symmetry is the same. The vertex of f(x) is (0, 0). The vertex of g(x) is translated up 2 units to (0, 2).
The graph of g(x) is wider than the graph of f(x). The graph of g(x) opens upward, and the graph of f(x) opens upward. The axis of symmetry is the same. The vertex of f(x) is (0, 0). The vertex of g(x) is translated down 2 units to (0, –2).
The graph of g(x) is wider than the graph of f(x). The graph of g(x) opens downward, and the graph of f(x) opens upward. The axis of symmetry is the same. The vertex of f(x) is (0, 0). The vertex of g(x) is translated down 2 units to (0, –2).