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Math Help - Graph equation by hand

  1. #1
    Senior Member euclid2's Avatar
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    Graph equation by hand

    y=-1/3(x-2)squared+1
    I know the co-ordinates of the vertex are (2,1), I just do not know how to graph this by hand.
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  2. #2
    Moo
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    A Cute Angle Moo's Avatar
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    Hello,

    You can do it this way :

    - graph y=x. (I guess you know how to do it... ?)

    - graph y=(x-2) by translating the graph of x of two units to the right (because x becomes x-2)

    - graph y=-1/3*(x-2) : multiplying by a constant. So the general appearance won't change, but because it's a negative constant, all the positive y will become negative, though the absolute value stays still. It's a symmetry to the x axis.

    - graph y=-1/3*(x-2)+1 : add 1 to the y, that is to say "elevate the curve of 1 unit"


    Does it look clear to you ?
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  3. #3
    Senior Member nikhil's Avatar
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    Find points where y=0.these two will lie on x axis.add them and divide it by 2 to get a third point.put this value in equation to get a particular point on y axis.now draw a rough sketch passing through these 3 points such that it make a U (distance between papallel lines will keep on increasing).I am giving a rough sketch so that you could check the nature your result..(the sketch that i am giving was not ment for your problem(you will get an inverted graph) but it will help you to understand the nature of graph).the point where graph take a turn is vertex.If still have any problem then ask.
    Attached Thumbnails Attached Thumbnails Graph equation by hand-16072008-003-.jpg  
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  4. #4
    Senior Member euclid2's Avatar
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    I know that the sketching pattern for parabolas seems to be over 1 up 1 over 1 up 3 over 1 up 5, and so on, and if there is a number infront of the x(a), then do we not just multiply the sketch pattern from over 1 up one to over 1 up 1/3, and so on?
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  5. #5
    Senior Member nikhil's Avatar
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    Hi!euclid2
    the method that I have given is for general quadratic equation.
    Other method for this particular question is graph shift.in this we just manipulate graph accordingly.
    But the method that I gave previously is a general method for quadratic equations
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