11'1 Parabolas

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11.1 Parabolas

• A parabola is the set of all points, (x,y),
  equidistant from a fixed line, (directex), and a
  fixed point, focus.
• The vertex is the midpoint of the segment from
  the focus perpendicular to the directex.
• The axis is the line passing through the focus
  and the vertex.
• Standard form
• x2 4py focus (0,p) directex y -p
• Parabola curves around the y-axis, vertical
  axis, x 0.
• y2 4px focus (p,0) directex x -p
• Parabola curves around the x-axis, horizontal
  axis, y 0.

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Graphs
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Example 1 Vertical Axis
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Example 2 Horizontal Axis
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Parabola Sketching

• Parabolas in this section will be approximate
  sketches.
• To get exact sketches you can use a t-table as
  learned in chapter 2.
• All parabolas in this section will have a vertex
  of (0,0).
• For the approximate sketches in this section
• Plot the focus point.
• Plot the line that is the directex.
• Starting at the vertex, (0,0), sketch the
  parabola.

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Example 3