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14 November, 06:32

For what values of m does the graph of y = 3x2 + 7x + m have two x-intercepts?

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Answers (2)
  1. 14 November, 06:36
    0
    So we see the leading coefient is positive (the 3 in the 3x^2 is positive) so the paraobola opens upward

    so for it to have 2 x intercepts, we must have the vertex below the x axis

    we must have the y value of the vertex negative

    so

    a hack is this

    to move a function up c units, add c to whole function

    also

    for

    y=ax^2+bx+c

    the x value of the vertex is - b/2a

    the y value is found by subsituting that value for x

    so

    y=3x^2+7x+m

    x value of vertex is

    -7 / (2*3) = - 7/6

    if we sub it in

    y=3 (-7/6) ^2+7 (-7/6) + m

    y=49/12-49/6+m

    we want the y value to be less than 0

    so

    0>49/12-49/6+m

    0>49/12-98/12+m

    0>-49/12+m

    49/12>m

    so it will have 2 x intercept for all m such that m<49/12
  2. 14 November, 06:51
    0
    The answer is C. m < 49/12
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