10.2 parabolas
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10.2 parabolas

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10.2 parabolas 10.2 parabolas Presentation Transcript

  • Properties of Parabolas Every point on a parabola is equidistant froma point called the focus and a line called thedirectrix. The directrix isperpendicular to the lineof symmetry. The vertex is halfwaybetween the focus anddirectrix.
  •  Parabolas can open vertically or horizontally.x2 = 4py y2 = 4px[Equations only good for vertex at (0, 0).]
  • To Graph: Determine if the axis of symmetry is verticalor horizontal. Find and graph the focus and directrix. Solve for the squared variable, then find p. Make a table of values and plot points. Connect with a curve. View slide
  • Example: Identify the focus and directrix of theparabola given by and draw theparabola. View slide
  • Example: Identify the focus and directrix of theparabola given by and draw theparabola.
  • Your Turn! Identify the focus and directrix of theparabola given by and draw theparabola.
  • Writing an Equation Use the equation of the directrix to find p. Remember: y = -p or x = -p Plug that value of p into the standardequation:x2 = 4py for vertical axis of symmetryy2 = 4px for horizontal axis of symmetry
  • Example: Write an equation of the parabola shown.
  • Example: Write an equation of the parabola shown.
  • Your Turn!Write an equation of the parabola shown.
  • Parabolas in Real Life Rays that are parallel to the axis of symmetryof a parabolic reflector are all directed to thefocus. Ex: Satellite dishes Rays emitted from thefocus are reflected inrays parallel to the axisof symmetry. Ex: Flashlights
  • Example: A reflector for a satellite dish is parabolic incross section, with the receiver at the focus.The reflector is 1 ft. deep and 20 ft. widefrom rim to rim. Write an equation for the cross section of thereflector. How far is the receiver from the vertex of theparabola?