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Math Help - modulus functions and trasformations of graphs

  1. #1
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    Question modulus functions and trasformations of graphs

    hey im stuck on this question

    The graph of y=|2x-4| + k touches line y=x at only one point. find values of constant k

    thanks
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  2. #2
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    Quote Originally Posted by elliegurl View Post
    hey im stuck on this question

    The graph of y=|2x-4| + k touches line y=x at only one point. find values of constant k

    thanks
    HI

    [|2x-4|+k]^2=[x]^2

    (2x-4)^2+2(2x-4)(k)+k^2=x^2

    3x^2+(4k-16)x+k^2-8k+16=0

    b^2-4ac=0 because it touches only at one point .

    Solve

     <br />
(4k-16)^2-4(3)(k^2-8k+16)=0<br />
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  3. #3
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    thankyou so much

    i do have another questions about real roots that im stuck on too

    show f(x)=4 has no real roots.. f(x)=3-|2x-1|

    i've ended up with a eq of -|2x-1|=1 is that right if it is what do i do next lol
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  4. #4
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    Quote Originally Posted by elliegurl View Post
    thankyou so much

    i do have another questions about real roots that im stuck on too

    show f(x)=4 has no real roots.. f(x)=3-|2x-1|

    i've ended up with a eq of -|2x-1|=1 is that right if it is what do i do next lol
    4=3-|2x-1|

    1=-|2x-1|

    Similar to your pervious question , square both sides to get rid of the modulus , then use b^2-4ac<0 since it has NO real roots . Give it a try !
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