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Math Help - Transformation

  1. #1
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    Transformation

    Suppose for the moment that b^2-4ac >0, So that f(x) has two distinct real roots , and a>0.

    A) Consider the transformation f(x)----> f(x)+k. What is the value of K such that f(x)+k has two identical real roots: Hint, you will need to complete squares.


    B) What is the condition on f(x)=ax^2+bx+c such that f(x) -----> f(-x) leaves the function unchanged? Hint: draw a picture of a quadratic function that does not change under this transformation. What kind of transformation is this?

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  2. #2
    Junior Member bondesan's Avatar
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    For A:

    If f(x)=ax^2 + bx + c, then f(x)+k = ax^2 + bx + (c+k).

    Two identical roots: \dfrac{\sqrt{b^2 - 4a(c+k)}}{2a} = 0.

    For B:

    I don't know precisely what do you mean in "leaving the function unchanged", but I guess you are looking for a condition that makes f(x)=f(-x). So what do we need for ax^2+bx+c=a(-x)^2 + b(-x) + c?
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  3. #3
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    Thank You very much, that really helps
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