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Math Help - Graphing Transformation

  1. #1
    rabidzebu
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    Graphing Transformation

    Does anybody know how to do transformations for variations of y=x^2 such as variations from the parent graph of y=x(x-2)(x+2)?

    On other y=x^2 graphs you can do: y=(x-2)^2 to move the graph 2 to the right, etc... I was wondering, what is the general rule for movment and transformation of y=x(x-2)(x+2)?

    Thanks

    (math test tommorow, ahhgg, i put this a couple places, but didn't realize there was a designated urgent section. sorry, i'm new)
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rabidzebu View Post
    Does anybody know how to do transformations for variations of y=x^2 such as variations from the parent graph of y=x(x-2)(x+2)?

    On other y=x^2 graphs you can do: y=(x-2)^2 to move the graph 2 to the right, etc... I was wondering, what is the general rule for movment and transformation of y=x(x-2)(x+2)?

    Thanks

    (math test tommorow, ahhgg, i put this a couple places, but didn't realize there was a designated urgent section. sorry, i'm new)
    well, graphing y=x(x-2)(x+2) is not really done by transformations.

    Looking at the formula, you notice y = 0 when x = 0, or x = 2 or x = -2, so these are your x-intercepts. so draw these lines on your graph, where they cut the x-axis is where y=x(x-2)(x+2) will cut the x-axis. then plug in numbers in the different intervals.

    you will have the interval (-inf, -2) and (-2, 0) and (0, 2) and (2, inf). when you plug in an x in each interval, you will get a positive or negative number. if the number is positive, the graph is above the x-axis in that interval, if the number is negative, the graph is below the x-axis in that interval. so for

    (-inf, -2) plug in x = -3 for example, you get y = -15 < 0, the graph is below the x-axis

    (-2, 0) plug in x = -1 for example, you get y = 3 > 0, the graph is above the x-axis

    (0, 2) plug in x = 1 for example, you get y = -3 < 0, the graph is below the x-axis

    (2, inf) plug in x = 3 for example, you get y = 15 > 0, the graph is above the x-axis

    now hopefully you know what shape the graph will have, when expanded you will get an x^3 graph, so you will have two turns, and one end going to + infinity and the other going to -infinity

    The graph is below. you should study all the transformation rules in your text book. texts books usually have the rules in one highlighted section
    Attached Thumbnails Attached Thumbnails Graphing Transformation-graph.jpg  
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