Question

Given the equation y=-(x+4)^2-6, what is the vertex and Axis of Symmetry (AOS)?

a) Vertex: (-4, -6), AOS: x = -4
b) Vertex: (-4, 6), AOS: y = -6
c) Vertex: (4, 6), AOS: x = 4
d) Vertex: (4, -6), AOS: y = -4

Answer 1

The vertex of the equation y=-(x+4)^2-6 is (-4, -6), and the axis of symmetry is x = -4.

Step-by-step explanation:

The equation given is y = -(x + 4)^2 - 6. To find the vertex and axis of symmetry, we can rewrite the equation in vertex form, which is y = a(x - h)^2 + k where (h, k) is the vertex. In this case, a = -1, h = -4, and k = -6. Therefore, the vertex is (-4, -6). The axis of symmetry is a vertical line that passes through the vertex. So, the axis of symmetry is x = -4.