Parabolas: Focus and Directrix (Algebra 2)
Free printable Algebra 2 worksheet on parabolas: reading the vertex, direction, focus and directrix from (x - h)² = 4p(y - k), and writing the equation from a focus and directrix.
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Algebra 2 · Math worksheet
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Conic Sections: Parabolas, Focus and Directrix
Use the relationship (x - h)² = 4p(y - k) (or its horizontal form). Read the vertex, direction, focus and directrix from each equation, or build the equation from a given focus and directrix.
- 1.For the parabola (x - 1)² = -8(y + 1), state the vertex, the direction it opens, the focus, and the directrix.
- 2.For the parabola (y + 1)² = -8(x - 2), state the vertex, the direction it opens, the focus, and the directrix.
- 3.For the parabola (x + 1)² = -4(y - 4), state the vertex, the direction it opens, the focus, and the directrix.
- 4.For the parabola (y - 3)² = 8(x - 1), state the vertex, the direction it opens, the focus, and the directrix.
- 5.For the parabola (x + 3)² = -4(y + 1), state the vertex, the direction it opens, the focus, and the directrix.
- 6.For the parabola (y - 1)² = -8(x - 3), state the vertex, the direction it opens, the focus, and the directrix.
- 7.A parabola has focus (-4, -5) and directrix y = -1. Write its equation in standard form.
- 8.A parabola has focus (-2, -1) and directrix x = 2. Write its equation in standard form.
- 9.A parabola has focus (-1, 0) and directrix y = 4. Write its equation in standard form.
- 10.A parabola has focus (1, 1) and directrix x = -1. Write its equation in standard form.
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