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How to find a quadratic function from a table of values?

  1. Oct 23, 2016 #1
    HI! I'm not sure if this can go in precalculus or not because I'm from Australia, and our Maths subjects don't get that specific until university level.
    1. The problem statement, all variables and given/known data

    For my assignment on quadratic functions, I have to find the equation (the the form of ax^2+bx+c) for a table of values?

    2. Relevant equations
    I know how to use vertex form and change from vertex form to standard form and vice-versa
    I have the co-ordinates:
    (1,3)
    (2,6)
    (3,10)
    (4,15)

    3. The attempt at a solution
    I think that I need to change it to vertex form, but I don't know how to do that, and I've spent the past couple of days trying to figure it out

    Thanks in advance
    Tris
     
  2. jcsd
  3. Oct 23, 2016 #2
    It has been a while since I've done anything like this, but the way I would go about solving this would be to plug the values of x into each equation to get the coefficients for each constant and then solving that as a system of equations. ex. (2,6) => a(2)^2+b(2)+c=6 => 4a+2b+c=6
     
  4. Oct 23, 2016 #3

    Simon Bridge

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    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    I think you need a clear statement of what the problem is and what information you have. Unless you can be specific, you won't be able to solve the probelm. Pretend you are explaining the problem to someone who has not done Aussie maths courses - be as standard as possible.
    You stuck a question mark on the end - do you not know?
    Please type out the exact problem statement ... do you have a table of values given to you and you have to find which quadratic function best fits it? Or maybe you have to construct a table of values that people can look up to figure out which quadratic form they are dealing with ... ??

    I see you have a bunch of coordinates - what are those coordinates of ?
    ie. are they coordinates of points that are on the quadratic form?
    Since you have a unary quadratic form and pairs of numbers ... you could just substitute the pairs into the general form and get the specific equation.

    ... but earlier you said:
    ... which seems contradictory.
    The result is we cannot know, with any confidence, what you are trying to describe.

    Note: I'm in New Zealand.
     
  5. Oct 23, 2016 #4

    jedishrfu

    Staff: Mentor

    You could construct a set of linear equations in three unknowns a, b, and c by subbing in each point to get one of the equations and then use linear algebra to reduce it or use some prior method of subbing to reduce a out then b out to get c...
     
  6. Oct 23, 2016 #5

    Mark44

    Staff: Mentor

    The problem as stated seems pretty clear to me.
    The equation would be y = ax^2 + bx + c.
    No, you don't need to put the equation in vertex form. Just do as jedishrfu suggests, and substitute the four pairs of x- and y-values into the equation y = ax^2 + bx + c. I've checked, and can verify that all four of the given points lie on the same parabola.
     
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