Algebra

Below is the graph of a polynomial function f with real coefficients. Use the graph to answer the following questions about f. All local extrema of f are shown in the graph.

I really need help with this one but I can't post the graph.

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  1. wherever it crosses the x axis is a zero so
    (x - xcrossing ) is a factor
    If it gets near the x axis but goes horizontal and veers away again, that is a complex root pair.
    like
    y = x^2 + 2 x + 4
    zeros at
    x = [ -2 +/-sqrt (4 - 16)]/2
    x = -1 +/- (1/2)sqrt (-12)
    = -1 +/- i sqrt 3

    where would that be horizontal (extrema)?
    0 = 2x + 2
    x = -1 at extrema (sure enough)

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  2. if it goes big +y for both big plus and minus x, then the first term is a x^even power
    if it is big minus for -x and big Plus for +x (or vice versa for - coefficient)then first term is x^odd power.

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