8) Graphing parabolas

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Conic Sections Parabolas
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Conic Sections
Conics Sections curves that are created by the
intersection of a plane and a right circular cone.
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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.
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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

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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.

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