Find the vertex, focus, directrix, and line of symmetry of y = 8(x – 5)2 + 2.
Hint
p equals 2, and the parabola opens up.
Answer
Vertex: (5, 2)
Focus: (5, 4)
Directrix: y = 0
Line of symmetry: x = 5
Find the vertex, focus, directrix, and line of symmetry for (y + 5)2 = -8(x + 4).
The y term is squared, and p is negative, so this parabola opens left.
Vertex: (-4, -5)
Focus: (-6, -5)
Directrix: x = -2
Line of symmetry: y = -5
Graph (y – 2)2 = 3(x + 1).
The y term is squared, and p is positive, so this parabola opens right. The focus will be to the right of the vertex.
Convert y2 + 6y + 4x + 1 = 0 to the conic form of a parabola.
-4x = (y2 + 6y + 9) + 1 – 9
-4(x – 2) = (y + 3)2
Convert y = x2 – x – 1 to the conic form of a parabola.
y = (x2 – x + ¼) – 1 – ¼
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to the right of the vertex.
