Question

F(x) = -2(x – 4)² – 2

What would the vertex, axis of symmetry and increasing / decreasing be of the question above?

Answer 1

The vertex of the function is (4, -2), the axis of symmetry is x = 4, and the function is decreasing before x = 4 and increasing after x = 4.

Step-by-step explanation:

The given function is f(x) = -2(x - 4)² - 2.

To find the vertex, we need to rewrite the function in vertex form, which is f(x) = a(x - h)² + k, where (h, k) represents the vertex.

Comparing the given function to the vertex form, we can see that the vertex is at (h, k) = (4, -2).

The axis of symmetry is a vertical line that passes through the vertex. In this case, the axis of symmetry is x = 4.

The function is decreasing on the interval (-∞, 4) and increasing on the interval (4, ∞).