Results 1 to 3 of 3

Math Help - Find Equation Of Parabola

  1. #1
    Member
    Joined
    Jan 2007
    Posts
    162

    Find Equation Of Parabola

    I just need to know, how to find equation of a parabola and put it in the form of ax^2+bx+c just from reading of the graph.

    I can do this for graphs like these were it cuts the x-axis:


    but for graphs were it doesn't cut the x-axis:

    how would you find the equation?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,710
    Thanks
    630
    Hello, r_maths!

    I just need to know, how to find equation of a parabola
    and put it in the form of ax + bx + c just from reading the graph.

    I can do this for graphs where it cuts the x-axis.
    But for graphs were it doesn't cut the x-axis,
    how would you find the equation?
    Code:
              |
             *|                    *
              |
            A o(0,18)           C o(4,18)
              | *               *
              |    *    B    *
              |         o
              |       (2,10)
              |
              |
          - - + - - - - - - - - - - -
              |

    I assume that point B(2,10) is the vertex of the parabola.

    The parabola is symmetric to its axis: x = 2.
    . . Hence, there is a point C(4,18) symmetric to A(0,18).


    The parabola has the general equation: .y .= .ax + bx + c

    We can evaulate these coefficients, using the three given points.

    (0,18): .a0 + b0 + c .= .18 . . c = 18

    (2,10): .a2 + b2 + 18 .= .10 . . 4a + 2b .= .-8 .[1]

    (4,18): .a4 + b4 + 18 .= .18 . . 16a + 4b .= .0 .[2]


    Multiply [1] by -2: . -8a - 4b .= .16
    . . - . . . .Add [2]: .16a + 4b .= .0

    And we get: .8a = 16 . . a = 2

    Substitute into [1]: .8 + 2b .= -8 . .b = -8


    Therefore: .y .= .2x - 8x + 18

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2007
    Posts
    162
    Thanks Soroban
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: March 22nd 2011, 04:57 PM
  2. Find the equation of the parabola
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: December 2nd 2010, 06:50 PM
  3. Find the equation of the parabola
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: December 1st 2010, 06:59 PM
  4. Find an equation of the parabola?
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: March 19th 2010, 12:27 PM
  5. Find equation of the parabola
    Posted in the Geometry Forum
    Replies: 1
    Last Post: February 17th 2010, 11:04 AM

Search Tags


/mathhelpforum @mathhelpforum