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    Q. g(x)=x^2+2ax+2 ,xER

    find the range of g in terms of a


    i dont know how to work this out, can someone show me a step to step method on how to do this please. thankyou
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    differentiate to find the minimum

    2x + 2a = 0
    x = -a

    so the smallest value g(x) can be (i.e. the range) is -a (i think)
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    (Original post by Pheylan)
    differentiate to find the minimum

    2x + 2a = 0
    x = -a

    so the smallest value g(x) can be (i.e. the range) is -a (i think)
    the answer should be g(x)>/ 2-a^2
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    could complete the square to find min also.
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    (Original post by klgyal)
    the answer should be g(x)>/ 2-a^2
    yeah i'm not great at finding ranges
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    Complete the square!!!!!!!!!!!!!!!!!!!!!!!!!! !111111111111111111111111ONE!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!

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    (Original post by Pheylan)
    differentiate to find the minimum

    2x + 2a = 0
    x = -a

    so the smallest value g(x) can be (i.e. the range) is -a (i think)
    The smallest value g(x) can take isn't that, what it is is g(-a).
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    the answer should be g(x)>/ 2-a^2
    Indeed, the value of the formula at x = -a is 2-a^2. This is minimum because the coefficient of x^2 is positive.

    In general, the x coordinate of the min (or max) of the parabola ax^2+bx+c is x = -b/(2a).
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    (Original post by Slumpy)
    The smallest value g(x) can take isn't that, what it is is g(-a).
    ooh i see, thanks
 
 
 
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