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Math Help - How do you find the vertex???

  1. #1
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    Question How do you find the vertex???

    I'm working on graphing absolute value equations, and for one of my problems, I need to identify the vertex using two seperate system of equations; one for the x-coordinate, and one for the y-coordinate. I don't really understand how to do it, and my first attempt gave me the wrong answer. Does anyone understand how to do this? Any help would be appreciated.

    Equation #1: y=-|x-2|-12

    My work:
    x-coordinate ...............y-coordinate
    x=-|(0)-2| ..................y=-|x-2|-12
    x=-|-2| .......................y=-|(-2)-2|-12
    x=-(2) ........................y=-|-4|-12
    x=-2 ...........................y=-4-12
    ...................................y=-16

    I know that the y-coordinate is wrong, but I dont understand how to do the problem.

    Equation #2: y=|2x+4|+3

    My work:
    x-coordinate .......................y-coordinate
    x=|2(0)+4| .........................y=|2x+4|+3
    x=|0+4| ............................y=|2(4)+4|+3
    x=|4| ................................y=|8+4|+3
    x=4 ...................................y=|12|+3
    ..........................................y=15

    My apologies for all of the periods, I couldn't get it to space right.
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  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Hello mackenzie25
    Quote Originally Posted by mackenzie25 View Post
    I'm working on graphing absolute value equations, and for one of my problems, I need to identify the vertex using two seperate system of equations; one for the x-coordinate, and one for the y-coordinate. I don't really understand how to do it, and my first attempt gave me the wrong answer. Does anyone understand how to do this? Any help would be appreciated.

    Equation #1: y=-|x-2|-12

    My work:
    x-coordinate ...............y-coordinate
    x=-|(0)-2| ..................y=-|x-2|-12
    x=-|-2| .......................y=-|(-2)-2|-12
    x=-(2) ........................y=-|-4|-12
    x=-2 ...........................y=-4-12
    ...................................y=-16

    I know that the y-coordinate is wrong, but I dont understand how to do the problem.

    Equation #2: y=|2x+4|+3

    My work:
    x-coordinate .......................y-coordinate
    x=|2(0)+4| .........................y=|2x+4|+3
    x=|0+4| ............................y=|2(4)+4|+3
    x=|4| ................................y=|8+4|+3
    x=4 ...................................y=|12|+3
    ..........................................y=15

    My apologies for all of the periods, I couldn't get it to space right.
    The vertex will occur where the expression inside the absolute value symbols, |...|, has the value zero. From this, you can work out the value of x, and hence the value of y.

    So for equation #1:

    |x-2|=0

    \Rightarrow x = 2

    Plug this value of x into the equation for y:

    y = -|2-2| -12

    \Rightarrow y =0 -12

    \Rightarrow y = -12

    So the vertex is at (2,-12)


    And for #2:

    |2x+4|=0

    \Rightarrow 2x=-4

    \Rightarrow x = -2

    And so y = |2(-2)+4|+3

    \Rightarrow y = |0| +3

    \Rightarrow y = 3

    So the vertex is at (-2,3)


    Grandad
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