Translating the quadratic function 2 units down from its original vertex (0, -4) results in a new vertex at (0, -6), making the range all numbers greater than or equal to -6 (Option A).
The given quadratic function has its vertex at (0, -4). If the graph is translated 2 units down, the new vertex will be at (0, -6) because the translation involves shifting the entire graph vertically. The original vertex at (0, -4) is moved down by 2 units.
The range of a quadratic function is determined by the vertex and the direction it opens. Since the given quadratic function has a downward opening, the range extends downward from the vertex. The original range is all numbers greater than or equal to the y-coordinate of the vertex, which is -4. After the translation, the new range becomes all numbers greater than or equal to the new y-coordinate of the vertex, which is -6.
Therefore, the correct answer is option A: "All numbers greater than or equal to -6." This is because the downward translation shifts the entire graph downward by 2 units, and the new range includes all real numbers greater than or equal to the new y-coordinate of the vertex.
The question probable may be:
5. The vertex of the quadratic function shown on the grid below is at (0,-4). If the graph of this function is translated 2 units down, which of the following best describes the range of the resulting graph? A. All numbers greater than or equal to -6 B. All numbers less than or equal to -6 C. All numbers greater than or equal to -2 D. All real numbers -5