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Math Help - Help with graphing polynomials

  1. #1
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    Help with graphing polynomials

    Hi, new here.

    I was wondering how can you get a fourth degree polynomial with a graph that only has 1 turn?

    This is the problem: 5x^4 +15x^2 + 10

    I thought the number of turns (or "bumps" as my teacher calls them) could be determined by "n-1"; n being the exponent of the leading coefficient. So, I thought this questions should have 3 turns, because 4-1= 3.

    (Hope I used the correct names for things here. I usually get confused with math terminology.)
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  2. #2
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    [size=3]Hello, adaeze!

    Welcome aboard!

    Can you get a 4th degree polynomial with a graph that only has 1 turn?

    This is the problem: . y \:=\:5x^4 +15x^2 + 10

    I thought the number of turns is determined by n-1,
    . . n being the exponent of the leading term. , This is true (sort of).

    So, I thought this graph should have 3 turns.

    A quartic function, y \:=\:ax^4 + bx^3 + cx^2 + dx + e, can have three turns.

    . . and is shaped like: . \backslash / \backslash / \;\;\text{ or }\;\;/ \backslash / \backslash \

    But if some of terms are missing, some of the bumps may "smooth out".

    The extreme case is: y \:=\:x^4, which resembles a parabola.

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