Algebra-1

To match the graph with a minimum point at (5, 0), symmetric about x = 5, and opening upwards, we use the following analysis:

Vertex Location: The lowest point (minimum) of the function is at (5, 0). For an absolute value function f(x) =∣x − h∣+ k, the vertex is at (h, k). Here, h = 5 and k = 0.

Symmetry: The function is symmetric about x = 5. This confirms that the absolute value function must be ∣x − 5∣, since the absolute value function ∣x − h∣ is symmetric about x = h.

O...