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Question 239721: Identify the coordinates of the vertex, and focus, the equations of the axis of symmetry and directirix, and the directions of opening of the parabola with the given equation. Then find the length of the latus rectum and graph the parabola.
-2(y-4)=(x-1)^2
I'm confused on each part, in general. Can you help me on each step?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Identify the coordinates of the vertex, and focus, the equations of the axis of symmetry and directirix, and the directions of opening of the parabola with the given equation. Then find the length of the latus rectum and graph the parabola.
-2(y-4)=(x-1)^2
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Form: (x-h)^2 = 4p(y-k)
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Your Problem:
(x-1)^2 = -2(y-4)
h = 1 ; k = 4 ; p = -1/2
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Vertex: (1,4)
The parabola opens downward:
Focus: (1,4-1/2) = (1,3.5)
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Axix of symmetry: x = h = 1
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Directrix: y = 4+1/2 = 4.5
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Length of Latus Rectum: |4p| = 2
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Graph:
-2(y-4)=(x-1)^2
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y = (-1/2)(x-1)^2+4
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Cheers,
Stan H.
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