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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
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    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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