10-3 Parabolas

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10-3 Parabolas

• What? Again?

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Psst hey didnt we see parabolas before?

• In section 2-8 we graphed parabolas by plotting
  points, because we were looking at parabolas as
  functions that could describe real world
  situations (ah, the dreaded word problem). Now,
  we will look at the same parabola in a slightly
  different way, as a Conic Section (circle,
  ellipse, hyperbola)

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The definition

• Of course! We need the definition first!
• The set of all points in a plane equidistant from
  a point (focus) and a line (directrix).

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Parabola Up/Down
focus
4c
Vertex (h,k)
c
c
directrix
What if 4c lt 0?
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Left/Right
Vertex (h,k)
4c
c
c
focus
directrix
What if 4c lt 0?
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FYI

• The book calls it 4p instead its the same
  thing. Other books have different versions of
  these equations, such as
• You can always convert it to a form you prefer. I
  prefer the one Ive given you.

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So what do we do with this?

1. Complete the square and get it in conic form (but
   only if there is a linear term for x and/or y).
2. Identify vertex and c.
3. Put focus, directrix, two points (width at focus)
   and AOS on the graph. Label these only. No
   tables or plotting 5 points this time. ?

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Examples
4. Find the equation of the parabola with focus
at (1, 5) and directrix at y 9
Homework Change pg 663 15, 17, 18, 20, 29, 30,
37, (graph the last 3)