8) Graphing parabolas - PowerPoint PPT Presentation

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8) Graphing parabolas

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directris, focus and vertex – PowerPoint PPT presentation

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Updated: 7 September 2014
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Title: 8) Graphing parabolas


1
Conic Sections Parabolas
2
Conic Sections
Conics Sections curves that are created by the
intersection of a plane and a right circular cone.
3
Conic Sections
Conics Sections curves that are created by the
intersection of a plane and a right circular cone.
4
Conics Sections
Conics Sections curves that are created by the
intersection of a plane and a right circular cone.
5
Conic Sections
Conics Sections curves that are created by the
intersection of a plane and a right circular cone.
6
Parabola
Focus (always inside)
  • Algebraic definition
  • All points that are equidistant from a line
    called the directrix and a fixed point called the
    focus

Both are same length
Both are same length
Directrix (always outside)
Applet
7
Axis of symmetry
  • The line through the focus perpendicular to the
    directrix is called the axis of symmetry of the
    parabola. Creates symmetrical halves

8
VERTEX
  • The point halfway between the focus and the
    directrix lies on the parabola.
  • It is the most extreme point, up or down, left or
    right.

9
Vertical Parabola Y a(x h)2 k
Maximum (the highest point)
Minimum (the lowest point)
The axis of symmetry is vertical
10
Horizontal Parabolax a(y k)2 h
The axis of symmetry is horizontal
11
Vertical Horizontal
Equation
Axis of Symmetry
Vertex
Focus
Directrix
Direction of opening
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