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Homework Help: Zeros, x intercepts, passing through x axis or just touching it.

  1. Jul 25, 2012 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
    So this isn't a specific question, I'm just having trouble with my definitions.

    In my book for f(x) = (x - 2) ((x + 1)^2) (x-4) it says that the zeros are at x = 2, -1, 4.

    On the page it shows that the graph doesn't cross the x axis at -1. Does that mean that some zeros cross the x axis and that some don't? Does -1 count as a zero?

    Are all x intercepts zeros? Meaning that x intercepts don't necessarily cross the x axis either? My book refers to the graph 'bouncing off' at points where the graph doesn't go through a point on the x axis (where y= 0).

    So if I'm asked for an x intercept, I can give a value for x where the line only just touches x on the x axis and doesn't also go through and past x?
  2. jcsd
  3. Jul 25, 2012 #2


    Staff: Mentor

    The zeroes don't cross the axis - they are just numbers on the axis. At a zero, a curve can cross or just touch the x-axis. A zero of a function is a number c such that f(c) = 0. Since f(-1) = 0 for your function, then -1 is a zero.
    All x-intercepts of a graph occur at the zeroes of the function. X intercepts are just points on the x-axis, so they don't cross it.
  4. Jul 25, 2012 #3
    Thanks for another great reply.
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