Final answer:
To find the vertex and axis of symmetry for the parabola -8(y+1)=(x+3)², rewrite the equation in vertex form. The vertex is (-3,-1) and the axis of symmetry is x = -3.
Step-by-step explanation:
To find the vertex and axis of symmetry for the parabola -8(y+1)=(x+3)², we need to first rewrite the equation in vertex form. The vertex form of a parabola is given by (x-h)² = 4a(y-k), where (h,k) represents the vertex of the parabola. So, let's rewrite the given equation:
-8(y+1) = (x+3)²
Divide both sides by -8:
(y+1) = -1/8(x+3)²
The vertex form of the equation tells us that the vertex is at the point (h,k), where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex. By comparing the rewritten equation with the vertex form, we can see that h = -3 and k = -1.
Therefore, the vertex of the parabola is (-3,-1).
So, the equation of the axis of symmetry is x = -3.