Question

Please help me, thank you

Answer 1

The vertex of the function f(x) =
`(1)/(16)` |x + 8| - 4 is (-8, -4), and the axis of symmetry is x = -8. The function is a vertically compressed absolute value graph shifted downward.

The given function is f(x) =
`(1)/(16)` |x + 8| - 4.

The absolute value function |x + 8| has its vertex at (-8, 0). In this case, the coefficient
`(1)/(16)` vertically compresses the graph, and the constant term -4 shifts it downward.

1. Vertex:

- The vertex form of the absolute value function is f(x) = a |x - h| + k, where (h, k) is the vertex.

- For f(x) =
`(1)/(16)` |x + 8| - 4, the vertex is (-8, -4).

2. Axis of Symmetry (AOS):

- The axis of symmetry for any function in the form f(x) = a |x - h| + k is x = h.

- Therefore, for the given function, the axis of symmetry is x = -8.

So, the vertex is (-8, -4), and the axis of symmetry is x = -8.