Algebra.Com's Answer #172117 by Theo(13342)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
As far as I can tell, the crossing points are:\r
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document.write( "x = -1, x = 2, x = 3\r
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document.write( "This would be calculated as follows:\r
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document.write( "Set the equation to 0 to get:\r
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document.write( "2(x+1)(x-2)^3(x-3)^2 = 0\r
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document.write( "Divide both sides by 2 to get:\r
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document.write( "(x+1)(x-2)^3(x-3)^2 = 0\r
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document.write( "This equation will be true if:\r
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document.write( "x+1 = 0 or (x-2)^3 = 0 or (x-3)^2 = 0\r
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document.write( "This makes:\r
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document.write( "x = -1 or x = 2 or x = 3\r
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document.write( "If you plug any one of these values into the equation, then the equation will be true which means that the graph of the equations touches the x-axis at those points.\r
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document.write( "You said:\r
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document.write( "By just looking at the function I
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document.write( "came up with (-1,0),(2,0),(3,0)
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document.write( "My professor listed (-1,0),(2,0)
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document.write( "as correct answers.
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document.write( "Isn't (3,0) part of the coordinates? \r
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document.write( "Looks like you are correct in that the equation touches the x-axis at those points.\r
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document.write( "It appears your professor might also be correct IF he is stating that the equation does not cross the x-axis at those points.\r
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document.write( "It touches at x = 3, but it does not cross.\r
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document.write( "Check the following graphs out to see what I mean:\r
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document.write( "The graph on the left is a long range view.\r
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document.write( "The graph on the right is a close in view.\r
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document.write( "Graph of your equation\r
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document.write( "It may be semantics, but it does not appear that the equation CROSSES the x-axis at x = 3, even though it TOUCHES the x-axis at x = 3.\r
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document.write( "I believe that's what he's saying.\r
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document.write( "If you were solving for the roots of the equation, which is defined as the point where the equation crosses the axis, then you would be correct in including x = 3. Otherwise a quadratic equation that has only one root would not be valid because it technically doesn't cross the x-axis at that point, but touches it, as is the case with this equation.\r
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document.write( "That's the only reason for the discrepancy that I can think of.\r
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document.write( "I would say that x = 3 IS an intercept, but that's only my opinion. The graph definitely TOUCHES the x-axis at x = 3 and that's a valid intercept point when dealing wth quadratic equations from everything I've seen so far.\r
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