Find the vertex, focus, and directrix of the parabola with the given equation.
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A)vertex: (2, -3)focus: (1, -3)directrix: x = 3
B)vertex: (-2, 3)focus: (-3, 3)directrix: x = -1
C)vertex: (-3, 2)focus: (-4, 2)directrix: x = -2
D)vertex: (2, -3)focus: (3, -3)directrix: x = 1

Question

Find the vertex, focus, and directrix of the parabola with the given equation.
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A)vertex: (2, -3)focus: (1, -3)directrix: x = 3 
B)vertex: (-2, 3)focus: (-3, 3)directrix: x = -1 
C)vertex: (-3, 2)focus: (-4, 2)directrix: x = -2 
D)vertex: (2, -3)focus: (3, -3)directrix: x = 1

Quizplus · Accepted Answer

The vertex form of a parabola is (x - h)^2 = 4p(y-k), where (h,k) is the vertex, p is the distance from the vertex to the focus (and from the vertex to the directrix), and the parabola opens either up or down depending on the sign of p. 
In this case, we have (x - 2)^2 = -8(y + 3), which tells us that the vertex is (2, -3) and p = -2. Therefore, the focus is 2 units to the left of the vertex, giving us (1, -3). The directrix is also 2 units to the right of the vertex, giving us x = 3.

Find the Vertex, Focus, and Directrix of the Parabola with the Given