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Math Help - Proving functions

  1. #1
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    Proving functions

    Hey all, I just have a homework problem example that I can't even begin.

    it says:

    Prove {-x^2+6x-8 x is in Reals} = (- , 1]


    I'm not even sure what to do, even looking in my notes and online didn't really help me, thought I'd give this place a try, thanks guys!
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  2. #2
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    Quote Originally Posted by teacast View Post
    Hey all, I just have a homework problem example that I can't even begin.

    it says:

    Prove {-x^2+6x-8 x is in Reals} = (- , 1]


    I'm not even sure what to do, even looking in my notes and online didn't really help me, thought I'd give this place a try, thanks guys!
    You are asked to find the range of the function:

    y = -x^2+6x-8 = -(x^2-6x+8) = -(x^2-6x+9-1)= -((x-3)^2-1)=-(x-3)^2+1

    The graph of the function is a parabola opening down, thus the vertex V(3, 1) is the maximum point and all values of y are equal or smaller than 1. Therefore y\in (-\infty,\ 1]
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  3. #3
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    Oh okay, just one question... why did you add a -1 to -(x^2-6x+9-1)? Just a way to say adding 8 so you could make it factorable?

    Thanks for the help!
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  4. #4
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    Quote Originally Posted by teacast View Post
    Oh okay, just one question... why did you add a -1 to -(x^2-6x+9-1)? Just a way to say adding 8 so you could make it factorable?

    Thanks for the help!
    He didn't' add -1 to anything. Her wrote the 8 as 9- 1 (which he can do because 8= 9- 1 so that he would have a perfect square, x^2- 6x+ 9= (x- 3)^2

    What he did is called "completing the square".
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  5. #5
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    ohhh okay okay, that's sort of what I meant, thanks for the clarification!
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