Final answer:
The vertex of the quadratic equation y = x² - 4 is found using the formula -b/2a, which yields the vertex (0, -4). The axis of symmetry is the vertical line x = 0, which passes through the vertex. Thus, option A) Vertex = (0, -4), Axis of Symmetry = x = 0 is correct.
Step-by-step explanation:
The question is asking to find the vertex and the axis of symmetry for the quadratic equation y = x² - 4. This equation is in the standard form of a quadratic equation, which is ax² + bx + c = 0, where a, b, and c are constants. In the given equation, a = 1, b = 0, and c = -4.
The vertex of a parabola in the form y = ax² + bx + c can be found using the formula -b/2a for the x-coordinate of the vertex. Since b = 0, the x-coordinate of the vertex is 0. To find the y-coordinate, substitute the x-coordinate back into the original equation, yielding y = (0²) - 4, which simplifies to y = -4. Therefore, the vertex of the parabola is (0, -4).
The axis of symmetry is a vertical line that passes through the vertex of the parabola and can be described by the equation x = h, where h is the x-coordinate of the vertex. Since the x-coordinate of the vertex is 0, the axis of symmetry is the line x = 0.
Based on our calculations, the correct answer is: Vertex = (0, -4), Axis of Symmetry = x = 0