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    Question: Sketch the graph of y=x^2-6x+3, giving the coordinates of the minimum point.

    Since I can't factorise it normally, I used the quadratic formula and got 3+root6 or 3-root6. I'm not sure how to continue from here. Do I sub the values into the quadratic to find the value of y for each one? Then the minimum point is the one lowest in the graph?
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    (Original post by Student1914)
    Question: Sketch the graph of y=x^2-6x+3, giving the coordinates of the minimum point.

    Since I can't factorise it normally, I used the quadratic formula and got 3+root6 or 3-root6. I'm not sure how to continue from here. Do I sub the values into the quadratic to find the value of y for each one? Then the minimum point is the one lowest in the graph?
    The x value of the minimum point is the mean of the two roots but this is a laborious way to find it. Do you know how to complete the square? This gives the coordinates of the minimum immediately.
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    (Original post by Mr M)
    The x value of the minimum point is the mean of the two roots but this is a laborious way to find it. Do you know how to complete the square? This gives the coordinates of the minimum immediately.
    Completing the square would give (x-3)^2 -6.
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    (Original post by Student1914)
    Completing the square would give (x-3)^2 -6.
    Yes so the coordinates of the minimum are (3, -6).

    In general, when y=(x-a)^2+b the minimum is (a, b).
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    (Original post by Mr M)
    Yes so the coordinates of the minimum are (3, -6).

    In general, when y=(x-a)^2+b the minimum is (a, b).
    What about for maximum point?
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    (Original post by Student1914)
    What about for maximum point?
    Completing the square gives the location of the maximum of a parabola too.

    http://www.mathcentre.ac.uk/resource...re1-2009-1.pdf
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    (Original post by Mr M)
    Completing the square gives the location of the maximum of a parabola too.

    http://www.mathcentre.ac.uk/resource...re1-2009-1.pdf
    Thanks!
 
 
 
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