Question

Find the vertex, focus, and directrix of the parabola.

A. Vertex: (0,0), Focus: (0,0), Directrix: y = -1
B. Vertex: (0,0), Focus: (0,0), Directrix: x = -1
C. Vertex: (0,0), Focus: (0,0), Directrix: y = 1
D. Vertex: (1,-2), Focus: (1,-2), Directrix: y = -1
E. Vertex: (0,-3), Focus: (0,-3), Directrix: x = 2

Answer 1

The vertex, focus, and directrix of the parabola is Vertex: (0,0), Focus: (0,0), Directrix: x = -1. Option B is answer.

Step-by-step explanation:

The general form of a parabola is y = a(x-h)^2 + k, where (h, k) is the vertex. Option B is answer.

For the given options:

A. Incorrect, as the directrix should be a vertical line, not y = -1.

B. Correct. The vertex, focus, and directrix are all at (0,0) and x = -1.

C. Incorrect, as the directrix should be a vertical line, not y = 1.

D. Incorrect, as the vertex and focus do not match.

E. Incorrect, as the vertex and focus do not match.

Therefore, the correct answer is option B with Vertex: (0,0), Focus: (0,0), Directrix: x = -1.