10.1 Parabolas

1
10.1 Parabolas

• A parabola is the set of all points that are
  equidistant from a fixed point (focus) and a
  fixed line (directrix).
• y 1/(4p) x2
• Where the vertex is the origin
• the focus is at (0,p)
• the directrix is the line y -p
• If p is greater than zero, the parabola opens
  upward y 2x2
• If p is less than zero, the parabola opens
  downward y -1/8 x2

2

• The presence of h and k in the standard equation
  results in horizontal and vertical shifts
• of the vertex to the point (h,k).
• y 2 ¼ (x-1)2
• x - 5 6 (y2)2