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Homework Help: Intercepts and graphs

  1. Feb 8, 2010 #1
    Alright lets says for example we were to sketch y=(x-2)(x-3). You would find x intercepts and you would write it as x-2=0 OR x-3=0, thus x=2 OR x=3. Why do we use the word OR when we use both of the intercepts to sketch the graph anyway? Why cannot we use AND instead.
  2. jcsd
  3. Feb 8, 2010 #2


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    Re: Intercepts

    To find the x-intercepts, which is where y=0, when you have two variables multiplied together to equal zero, you only need one or the other to be 0.

    e.g. if you have ab=0, where a and b are not equal, then a can be 0 or b can be 0, but since a is not equal to b then you can't have a and b are 0.

    Same thing goes with that quadratic. (x-2)(x-3)=0 means that for some value x, the first factor (x-2) will equal zero while the second won't, and similarly for the second factor. This is why it is said x-2=0 OR x-3=0.
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