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Question:

pavelpimen
pavelpimen
Student
High School - 10th Grade

fm(x)=x^2 +7(m-1)x+m-1 is a family of functions.Which are m values so that the curves associated to the fm(x), have the vertex set above ox axis?

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Posted by pavelpimen on Wednesday June 3, 2009 at 5:07 AM and tagged with axis, curve, function, math, vertex.

Answers:

  1. neela
    neela Teacher
    Graduate School

    eNotes Editor

    f(m,x) = x^2+7m-1)x+m-1 . We shall write the right side as below.

    f(m,x)={x+7(m-1)/2}^2-[49(m-1)^2/2]^2-(m-1)]

    ={x+7(m-1)/2}^2-(1/2){(m-1)(49m-53)}.

    The curve has its vertex at:

    x=-7(m-1)/2 and its y=f(m,-7(m-1)/2)) = (-1/2){m-1)(49m-53} which is positive if(m-1)(49m-53) is negative=>

    1<m<53/49.

    Therefore, the vertices of the family of curves will be above x axis if  f(m,-7(m-1)/2) is positive  and this can happen only  when the values of m lie between 1 and 53/49

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    Posted by neela on Wednesday June 3, 2009 at 10:53 AM