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In the equation: y = -(2 + 3)^2 - 1, find the vertex, focus, or directrix.

a) Vertex: (-2, -1), Focus: N/A, Directrix: N/A
b) Vertex: (-3, -1), Focus: N/A, Directrix: N/A
c) Vertex: (-2, -1), Focus: N/A, Directrix: y = -2
d) Vertex: (-3, -1), Focus: (-3, -1), Directrix: y = -2

1 Answer

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Final answer:

The given equation simplifies to y = -26, representing a parabola parallel to the x-axis, thus eliminating options of the focus or directrix. The correct answer is b) Vertex: (-3, -1), Focus: N/A, Directrix: N/A as the equation does not contain an x to influence the vertex coordinates.

Step-by-step explanation:

The equation given is y = -(2 + 3)^2 - 1. To find the vertex of this equation, we see that it represents a parabola in the form y = a(x - h)² + k where (h, k) is the vertex.

By simplifying the given equation, we have y = -5^2 - 1, which simplifies to y = -25 - 1 or y = -26. Since there is no x in the equation, this means the parabola is a line parallel to the x-axis and thus does not have a discrete focus or directrix like a traditional parabola does. Therefore, the correct answer is option b) Vertex: (-3, -1), Focus: N/A, Directrix: N/A.

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