Question

graph a (above), graph b (below). options: horizontal translation of -1; reflection over the x - axis; reflection over the y - axis; vertical translation of -1

Explanation:

First, identify the vertex of Graph A: it is at (2, 0), and the graph opens upward. The vertex of Graph B is at (2, 0), and it opens downward. A reflection over the x-axis transforms a function $f(x)$ to $-f(x)$, which flips the graph vertically, matching the change from Graph A to Graph B. Other options do not fit: a horizontal translation would shift the vertex left/right, a vertical translation would shift it up/down, and a y-axis reflection would flip the vertex to (-2, 0), none of which match the graphs.

Answer:

Reflection over the x-axis