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Quadratic equations?

  1. Jan 16, 2009 #1
    how do you calculate the equation of a quadratic curve. A straight line curve uses
    y-y1=m(x-x1) is i an alteration of this line?
  2. jcsd
  3. Jan 16, 2009 #2


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    Actually there are multiple ways of expressing lines, quadratics etc.

    The general form is
    [tex]y=ax^2+bx+c[/tex] where [tex]a\neq 0[/tex]
    This is efficient because it is translated into the quadratic formula easily.

    There is also the vertex form
    This form quickly gives the vertex (k,q) of the parabola.


    To calculate the equation of a quadratic, you need 3 points minimum. If you know it's a parabola then you will also know it can be expressed in the general form [tex]y=ax^2+bx+c[/tex]
    If one of the points given to you lie on the parabola, then the point satisfies the quadratic. i.e. you can substitute the x and y value of the point into the general form.
    Lets say its (2,3)
    Then [tex]3=4a+2b+c[/tex] which is a linear equation with 3 variables.
    Once you do this for all 3 points, you will have 3 equations with 3 variables. Thus, you can solve them simultaneously to find the values of a, b and c.

    These values can then be plugged back into the general form to give you your parabola.
  4. Jan 16, 2009 #3


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    Staff Emeritus
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    Those are the formulas for quadratic functions- whose graphs are parabolas with vertical axis. You can have parabolas at any angle to the axes but then they are not the graphs of functions.
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