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Math Help - Adding a Linear Function to a Quadratic Graph

  1. #1
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    Adding a Linear Function to a Quadratic Graph

    Hello

    I am wondering how i establish where to draw this line?

    Question
    22
    The grid opposite shows the graph of y = x2 + 3x 2
    (a) By drawing an appropriate straight line on the graph solve the equation

    x
    2 + 3x 3 = 0
    .................................................. .................................................. ............................................
    .................................................. .................................................. ............................................
    Answer .................................................. ........................
    (2 marks)

    (b) By drawing an appropriate straight line on the graph solve the equation
    x2 + 2x 1 = 0

    graph can be seen on page 22 here:

    http://store.aqa.org.uk/qual/gcse/qp...W-QP-JUN05.PDF
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  2. #2
    MHF Contributor red_dog's Avatar
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    Medgidia, Romania
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    Let f(x)=x^2+3x-2

    Then, g(x)=x^2+3x-3=x^2+3x-2-1=f(x)-1

    g(x)=0\Rightarrow f(x)=1

    So, draw a line parallel to Ox, through y=1 and the x-coordinates of the intersection points are the solutions of the equation.

    h(x)=x^2+2x-1=f(x)+x+1
     h(x)=0\Rightarrow f(x)=-x-1

    Draw the line y=-x-1 and the x-coordinates of the intersection points are the solutions of the equation.
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  3. #3
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    Great, thanks for your help
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