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Math Help - Polynomial function

  1. #1
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    Polynomial function

    The diagram below shows part of the graph of a polynomial function-
    A possible equation for the rule of the function is:
    The back of the book seems to think its y=(x-c)(b-x)^2 but i am pretty certain its y=(x+c)(x-b)^2. So am i wrong or is the book wrong?
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  2. #2
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    Quote Originally Posted by chaneliman View Post
    The diagram below shows part of the graph of a polynomial function-
    A possible equation for the rule of the function is:
    The back of the book seems to think its y=(x-c)(b-x)^2 but i am pretty certain its y=(x+c)(x-b)^2. So am i wrong or is the book wrong?
    That depends how you define the value of c:

    if c is a negative number then the book is correct

    if you define c as absolute value of c then you are right. But I don't see any reason why you should do that
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  3. #3
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    Hello, chaneliman!


    Their graph is misleading, but the book is correct.

    Consider the two intercepts anywhere on the x-axis.
    Code:
          |
          |                          *
          |           *
          |       *      *          *
          |    *           *      *
        - | -*- - - - - - - - -*- - - -
          |* c                 b
          |
         *|
          |

    The general form would be: . x-c)(x-b)^2" alt="y \:=\x-c)(x-b)^2" />
    . . no matter where the intercepts are.


    If I were still teaching, I'd use this trick question on my students.
    . . I'm just kidding . . . (Am I the only one laughing?)

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  4. #4
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    i still don't understand this. y can't it be y=(x+c)(x-b)^2.
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  5. #5
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    Quote Originally Posted by chaneliman View Post
    The diagram below shows part of the graph of a polynomial function-
    A possible equation for the rule of the function is:
    The back of the book seems to think its y=(x-c)(b-x)^2 but i am pretty certain its y=(x+c)(x-b)^2. So am i wrong or is the book wrong?
    Quote Originally Posted by chaneliman View Post
    i still don't understand this. y can't it be y=(x+c)(x-b)^2.
    First I'll point out that (x - b)^2 and (b - x)^2 are the same - you can expand and confirm this simple fact.

    Now ...... look at the given graph. Clearly a reasonable value of c could be c = -3, say. A reasonable value of b could be b = 2, say.

    You should have absolutely no problem in accepting that for these values of c and b, a possible rule for the graph is y = (x + 3)(x - 2)^2 = (x + 3)(2 - x)^2.

    Sub c = -3 and b = 2 into y = (x-c)(b-x)^2 and you get the same equation.

    BUT ...... Sub c = -3 and b = 2 into y = (x+c)(b-x)^2 and you DO NOT get the same equation ....
    You get y = (x - 3)(2 - x)^2. This is clearly wrong. The x-intercept is at x = 3, NOT x = -3.
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  6. #6
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    Quote Originally Posted by chaneliman View Post
    i still don't understand this. y can't it be y=(x+c)(x-b)^2.
    the general rule looks like that....

    (x - a)(x - b)^2

    because you must let what is inside the brackets equal to 0

    so x - a = 0 then x = a .... thats the value you are looking for

    e.g a = 5

    x - 5 = 0

    x = 5

    if the answer was -6

    x - (- 6) = 0

    x + 6 = 0

    x = - 6

    =] simple once you can understand it
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  7. #7
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    i think i get it. So the equation would change if it was as followed (i added a negative). Thanks guys
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