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write equation of a polynomial function with the given characteristics.
Leading coefficient is 1 or -1
crosses the x axis at -2,3, and 4
touches the x axis at 0
lies above the x axis between -2 and 0

  • algebra -

    from "touches the x axis at 0", we can see a double root of x=0 at the origin, meaning the curve must touch the x-axis at the origin without crossing.
    But it does cross at x = -2,3 and 4

    so we would have
    y = ±1(x^2)(x+2)(x-3)(x-4)

    [think of the x^2 as (x-0)(x-0)]

    make a sketch with intercepts as I have indicated, having the curve rise to infinity in the 1st, and to negative infinity in the 3rd quadrants,
    for the curve to be above the x-axis between -2 and 0
    so the coefficient has to be +1

    so y = (x^2)(x+2)(x-3)(x-4)

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