Vertex Points and Function Domain: Determining Ascending vs Descending Behavior

To know whether the domain of a function is ascending or descending, you need to know the vertex point.

To solve this problem, we need to determine whether knowing the vertex of a function $y = (x-p)^2$ allows us to conclude if the function's domain is ascending or descending.

Consider the vertex form of the given parabola: $y = (x-p)^2$.

• The parabolic function opens upward since the coefficient of $(x-p)^2$ is positive (1).
• The vertex of the parabola is $(p, 0)$.
• A parabola's opening direction is determined by the sign of the coefficient of the squared term. By understanding this, we ascertain that the function decreases towards the vertex (left side of vertex) and increases away (right side of vertex).
• Thus, the left side of $p$, as $x$ approaches the vertex, is descending, and to the right is ascending, confirming the vertex as a divider of these behaviors.

Overall, knowing the vertex allows us to describe the behavior of the function's graph as ascending or descending at and away from the vertex point, verifying the statement.

The conclusion is that the statement is True.