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Math Help - equation of a graph

  1. #1
    Member GAdams's Avatar
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    equation of a graph

    Bruce is given the graph of y = 3x - 2

    He is going to draw a second graph on the same axes.

    He wants the x-coordinates of the points of intersection of the two graphs to be the solutions to the quadratic equation x^2 + x - 7 = 0

    Work out the equation of the graph that needs to be drawn. Do not draw the graph.


    I have tried a few ways of doing this -not sure if I am right!

    Firstly:

    x^2 + x -7 = 3x - 2 and solved, but soon realised that this gave me the x-cocordinates but not the 'equation of the graph that needs to be drawn'.

    Secondly:

    adding the two equations and trying to solve as a pair of simultaneous equations -didn't get very far that way either.

    I'm a bit stumped, I'm not sure how I would go about tackling this kind of problem -help!
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  2. #2
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    Quote Originally Posted by GAdams View Post
    Bruce is given the graph of y = 3x - 2

    He is going to draw a second graph on the same axes.

    He wants the x-coordinates of the points of intersection of the two graphs to be the solutions to the quadratic equation x^2 + x - 7 = 0

    Work out the equation of the graph that needs to be drawn. Do not draw the graph.

    I have tried a few ways of doing this -not sure if I am right!

    Firstly:

    x^2 + x -7 = 3x - 2 and solved, but soon realised that this gave me the x-cocordinates but not the 'equation of the graph that needs to be drawn'.

    Secondly:

    adding the two equations and trying to solve as a pair of simultaneous equations -didn't get very far that way either.

    I'm a bit stumped, I'm not sure how I would go about tackling this kind of problem -help!
    Let the required graph have the equation y = ax^2 + bx + c. The intersection of this graph with y = 3x - 2 is found by solving ax^2 + bx + c = 3x - 2. Re-arrange this so that you can compare it with x^2 + x - 7 = 0. Hence get the values of a, b and c.
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  3. #3
    Member GAdams's Avatar
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    Quote Originally Posted by mr fantastic View Post
    Let the required graph have the equation y = ax^2 + bx + c. The intersection of this graph with y = 3x - 2 is found by solving ax^2 + bx + c = 3x - 2. Re-arrange this so that you can compare it with x^2 + x - 7 = 0. Hence get the values of a, b and c.
    I'm not sure what you mean by 're-arrange this' , is it this?:

     ax^2 + bx - 3x + c + 2 = 0 ?

    I can't see how this would work.
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  4. #4
    Member GAdams's Avatar
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    ooh, ooh, I think I got it....

    Is it:

    x^2 + 4x - 5 ??
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  5. #5
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    Quote Originally Posted by GAdams View Post
    ooh, ooh, I think I got it....

    Is it:

    x^2 + 4x - 5 ??
    I get c = -9 ....
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