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Math Help - describing tranformations

  1. #1
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    describing tranformations

    why does 3x^2+ 2x +14 get smaller when i do 3(-x)^2 + 2(-x) +14?

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    Last edited by chaneliman; February 9th 2008 at 05:37 PM.
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  2. #2
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    Quote Originally Posted by chaneliman View Post
    why does 3x^2+ 2x +14 get smaller when i do 3(-x)^2 + 2(-x) +14?

    Thanks
    It doesn't. g(x) = f(-x) = 3(-x)^2 + 2(-x) +14 is the reflection of f(x) in the y-axis. There will be some values of x for which f(x) > f(-x) and some for which f(x) < f(-x), since the line of symmetry of f(x) is NOT the y-axis. But f(-x) will not be smaller than f(x) for all values of x .....

    In fact:

    f(x) = f(-x) for x = 0

    f(x) < f(-x) for x < 0

    f(x) > f(-x) for x > 0

    Note also that each graph has the same minimum value of y, namely 41/3 ...... It occurs at x = -1/3 for y = f(x) and x = 1/3 for y = f(-x).
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