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  1. 1. Conic Sectionsand ParabolasChapter 8.1
  2. 2. Chapter 8.1• The study of conic sections, or simply conics.• Conics are formed by the intersection of a planewith a pair of cones.
  3. 3. ParabolasAlgebraically speaking• y = ax2 + bx + c• Has a U-shape.• Opens with upward or downward.• The lowest or highest point on such a parabola iscalled the vertex.• It is symmetric about the its axis called the axis ofsymmetry.
  4. 4. Parabolas
  5. 5. Parabolas
  6. 6. Standard Form• The Standard Form of the equation of a parabolawith vertex at (h, k) is:• (x - h)2 = 4p (y- k), vertical axis; directrix at y = k - p• (y - k)2 = 4p(x - h), horizontal axis; directrix at x = h - p• The focus lies on the axis p units from the vertex.• Find the standard form of the equation of theparabola with vertex (2, 1) and focus (2, 4)
  7. 7. Standard Form
  8. 8. Standard Form• Find the standard form of the parabola with vertexat the origin and focus (2, 0)
  9. 9. Parabola