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Notes #3-___ Date:______

Notes #3-___ Date:______. 8.1 Introduction to Conics: Parabolas (632).

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Notes #3-___ Date:______

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  1. Notes #3-___Date:______ 8.1 Introduction to Conics: Parabolas (632) Defined algebraically as the graphs of second degree (quadratic) equations in two variables: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, where A, B & C are not all 0.* Completing the square is used to get the standard equation. Generator Vertex Nappes (the two cones) Axis

  2. Page 633, Figure 8.2 Conic Sections (conics): Degenerate Conics: A circle is considered to be degenerate ellipse.

  3. Equations of Parabolas • General Form: y = ax2 + bx + c Vertex: y-intercept: • Standard Form: y = a(x – h)2 + k y – k = a(x – h)2 Vertex: The sign of “a” in both determines:

  4. Definition of a Parabola: • Algebra in Motion, Conics: parabola 1

  5. Page 634, Figure 8.3 p p

  6. Page 637 – Don’t copy this down, it’s in your book!

  7. Example 1: Always sketch the given information! Find the vertex, focus & directrix of: a) x2 – 6x – 4y + 5 = 0 b) y2 + 6y + 8x + 25 = 0 V(3, -1), f(3, 0) & y = -2 V(-2, -3), f(-4, -3) & x = 0

  8. Example 2: Write an equation in standard form if: a) Vertex: (4, 0) & directrix: x = 5 b) Focus: (2, 2) & directrix: x = -2 c) Vertex: (0, 0) & through (3, 5) y2 = -4(x – 4) (y – 2)2 = 8x 5x2 = 9y

  9. Page 639 • Reflective Property of a Parabola

  10. Example 3: The satellite dishes at the VLA are 82 feet in diameter. If they have a depth of 10.25 feet, how far from the vertex should the receiving antenna be placed? p = 41 feet

  11. Assignment • A#3-20: (641) #1-62 D2S2, 65-70

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