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    determine the coordinates of the points of intersection of the line y=x+11 and the curve y = x^2 + 10x +19
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    (Original post by ikrshafiq)
    determine the coordinates of the points of intersection of the line y=x+11 and the curve y = x^2 + 10x +19
    Both equations are y equals something. So set the two right-hand-sides of the equation equal to each other. You can simplify this to a quadratic and get x coordinates (there may be two). Then just substitute them into one of the original equations (use the simplest one ).
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    Put them into a linear equation and then solve:

    x+11=x^2+10x+19
    0=x^2+9x+8
    Put into double brackets: (x+1)(x+8)=0
    Solve to find the co-ordinates
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    (Original post by TheMindGarage)
    Both equations are y equals something. So set the two right-hand-sides of the equation equal to each other. You can simplify this to a quadratic and get x coordinates (there may be two). Then just substitute them into one of the original equations (use the simplest one ).
    is this correct:
    x+11=x^2 +10x+19
    x^2-9x+8
    (x-1)(x-8)=0
    x=1 or x=8
    and then subtiute it in y=x + 11 to get the y values
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    eyyyyy
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    (Original post by ikrshafiq)
    is this correct:
    x+11=x^2 +10x+19
    x^2-9x+8
    (x-1)(x-8)=0
    x=1 or x=8
    and then subtiute it in y=x + 11 to get the y values
    Should be +9x in the quadratic rather than -9x. You can double-check whatever answers you get by substituting into the other equation (y = x^2 + 10x +19) and checking whether you get the same.
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    (Original post by ikrshafiq)
    is this correct:
    x+11=x^2 +10x+19
    x^2-9x+8
    (x-1)(x-8)=0
    x=1 or x=8
    and then subtiute it in y=x + 11 to get the y values
    I think it should be:

    x+11=x^2+10x+19
    0=x^2+9x+8 (because of x^2+10x+19-x-11)
    0=(x+1)(x+8)
    So x=-1 and x=-8

    Then sub in to find y for each x value and you've got your coordinates
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    (Original post by Nikey)
    I think it should be:

    x+11=x^2+10x+19
    0=x^2+9x+8 (because of x^2+10x+19-x-11)
    0=(x+1)(x+8)
    So x=-1 and x=-8

    Then sub in to find y for each x value and you've got your coordinates
    which one do u have to sub in y=x+11 or y=x^2+10x+19
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    (Original post by yemenia16)
    which one do u have to sub in y=x+11 or y=x^2+10x+19
    any
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    (Original post by yemenia16)
    which one do u have to sub in y=x+11 or y=x^2+10x+19
    Any would work. I'd do y=x+11 because it's quicker and easier.

    So when x = -1, y=(-1)+11
    and when x = -8, y=(-8)+11

    And there's your 2 sets of coordinates.
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    the quadratic equation
    (2k -3)^2=2x+(k-1)=0
    where k is a constant, has real roots
    a. show that 2k^2 - 5k +12 equal < 0

    how would you do this guys???
 
 
 
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