Return to Video

www.mathcentre.ac.uk/.../alg-anim-1.mp4

  • 0:02 - 0:06
    Completing the square works
    because you can change one
  • 0:06 - 0:09
    parabola into another using
    standard transformations.
  • 0:11 - 0:13
    You can scale the parabola.
  • 0:15 - 0:18
    And you can move the parabola or
  • 0:18 - 0:20
    translate it. Horizontally.
  • 0:22 - 0:23
    All vertically.
  • 0:26 - 0:29
    You can also reflect the
    parabola. That's like a
  • 0:29 - 0:33
    scaling, but with the scale
    factor of minus one.
  • 0:35 - 0:41
    Now the standard quadratic
    expression Y equals X squared
  • 0:41 - 0:43
    gives this parabola.
  • 0:45 - 0:49
    And any other quadratic will
    always give a parabola, but it
  • 0:49 - 0:54
    will be a different size and be
    in a different place.
  • 0:55 - 1:02
    So to get this new parabola,
    we take the standard parabola
  • 1:02 - 1:09
    and 1st change its eyes instead
    of Y equals X squared. It's
  • 1:09 - 1:13
    now Y equals 1/2 X squared.
  • 1:16 - 1:22
    Next we move the parabola
    sideways instead of Y equals 1/2
  • 1:22 - 1:28
    X squared. The ex has become
    X minus 2.
  • 1:31 - 1:34
    And finally we move the parabola
  • 1:34 - 1:40
    vertically. We add on one
    to the formula and that
  • 1:40 - 1:44
    gives us the quadratic in
    completed square form.
Title:
www.mathcentre.ac.uk/.../alg-anim-1.mp4
Video Language:
English

English subtitles

Revisions