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Parabolas

Parabolas. p = a number that tells you where the focus and directrix are ( h.k ) = coordinates of the vertex Focus= point inside the parabola (add p to one coordinate of the vertex) Directrix = line behind the parabola The focus and directrix are equidistant from the vertex.

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Parabolas

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  1. Parabolas p = a number that tells you where the focus and directrix are (h.k) = coordinates of the vertex Focus= point inside the parabola (add p to one coordinate of the vertex) Directrix = line behind the parabola The focus and directrix are equidistant from the vertex If p is positive it opens up If p is negative it opens down If p is positive it opens right If p is negative it opens left

  2. To Graph Parabolas • Put it in standard form (Same variables on the same side. Factor and complete the square, if needed) • Decide whether it opens up/down/left/right • Plot vertex • Find focus (add p to vertex) and directrix • Use t-chart to find and plot 2 additional points • Graph

  3. Write the equation of the parabola in standard form. vertical, up Parabolas Vertex: (0, 0)

  4. GRAPH vertex: (0, 0) focus:(0, 2 ) di rectrix: y = - 2 X Y -4 2 4 2

  5. horizontal , left Vertex: (0, 0)

  6. GRAPH tex ver , (0, 0) focus: (-3, 0) di r ec trix : x = 3

  7. Graph. vertical, down h = 1 k = 2 p =? vertex: (1, 2) -4 = 4p p = -1

  8. Graph. vertex: (1, 2) directrix: y = 3 focus: (1, 1)

  9. Graph. horizontal, right 3 = -2 p =? h = k 8 = 4p vertex: (3, -2) 2 = p

  10. Graph. vertex: (3, -2) directrix: x = 1 latus: 8 focus: (5, -2)

  11. Graph. vertical, up h = -1 k p =? = -1 12 = 4p vertex: (-1, -1) 3 = p

  12. Graph. vertex: (-1, -1) directrix: y = -4 latus: 12 focus: (-1, 2)

  13. Not in Standard form? • Identify which variable is squared. Keep each term with that variable on the left. Move everything else to the right. • Complete the square with the left side. • Factor the left side. • On the right side, factor the lead coefficient out of both terms.

  14. Graph. complete the square factor vertical, down h = 1 k = 1 p = -1 vertex: (1, 1) directrix: y = 2 focus: (1, 0)

  15. Graph. vertex: (1, 1) directrix: y = 2 focus: (1, 0)

  16. Homework Page 178: 2 – 22 Even

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