Section 10-2 Pages 735-743

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Section 10-2Pages 735-743

• Introduction to Conics
• Parabolas

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Objectives

• I can write equations for parabolas in Standard
  Format
• I can graph parabolas by finding the key
  information for each
• I can complete the square to obtain vertex format

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How to identify types of Conic Sections from
General Form

• PARABOLAS CIRCLES
• Either x or y is x and y are both
• squared but not squared with the
• both. same coefficient.
• ELLIPSES HYPERBOLAS
• x and y are both x and y are both
• squared with different squared, 1 is positive
• coefficients but the 1 is negative.
• same signs.

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Conic Sections

• A conic section is the intersection of a plane
  and a double cone.

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Conical View
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Parabolas (10-2)
A Parabola is the set of all points in a plane
that are equidistant between a fixed point
(focus) and a line (directrix).
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Real Parabolas

• Flashlights
• Headlights
• Mirrors
• Projectile Motion
• Satellite Dish
• Architecture

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A Little Review

• You know the basic equation of any parabola as
• y ax2 bx c
• You can write this in vertex format and it
  becomes y a(x h)2 k
• In that format, the vertex is (h, k) and the
  axis of symmetry is x h
• In addition, if a gt 0, then the parabola opened
  upwards, if a lt 0 then the parabola opened down.

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Review Complete the Square

• Write y 2x2 12x 14 in vertex format
• y 2x2 12x 14 (Underline variables)
• y 2 (x2 6x) 14 (Factor out the 2)
• y 2 (x2 6x _____) 14 - _______
• y 2 (x2 6x 9) 14 18
• y 2 (x 3)(x 3) - 4
• y 2 (x 3)2 4
• Vertex (-3, -4)
• Axis of Sym x -3
• Opens Upward since a gt 0

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A New Review

• The new equation we look at is x ay2 by c
• The new basic equation of a parabola is
  x a(y k)2 h
• In that format, the vertex is (h, k) and the
  axis of symmetry is y k
• In addition, if a gt 0, then the parabola opened
  Right, if a lt 0 then the parabola opened Left.

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Parabola

• A parabola is a set of points in a plane that are
  all the same distance from a fixed line called
  the directrix and a fixed point not on the line
  called the focus .

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Vocabulary

• Any line segment that passes through the focus
  point with endpoints on the parabola is called a
  focal chord
• The perpendicular chord to the AOS is called the
  latus rectum(LR)

Latus rectum
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Key Concept

• The distance from Vertex Point to Focus Point is
  p
• This is also the same distance from Vertex Point
  to the Directrix Line

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Parabolas
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Where to find them

• FOCUS inside the parabola
• DIRECTRIX outside of the parabola
• AOS through the vertex, perpendicular to the
  directrix
• FOCAL CHORD (latus rectum) inside of the
  parabola

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When graphing you MUST label

• vertex
• focus
• directrix
• axis of symmetry
• endpoints of the focal chord

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Homework

• WS 10-1