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Graph x^24x+3 
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#1
Sep306, 02:32 PM

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Graph x^24x+3.
My question: 1) is 4x a slope? I'm trying to graph this equation w/out using a calculator or plugging in points. Thanks! 


#2
Sep306, 02:40 PM

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Do you know what kind of shape the graph has?



#3
Sep306, 02:52 PM

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Yes, a parabola.



#4
Sep306, 03:09 PM

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Graph x^24x+3
You might try completing the square, this should make it clear how it relates to the graph of the good old y=x^2.



#5
Sep306, 05:16 PM

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No, "4x" is not a slope. The slope of a line is a number. If y= mx+ b then the slope is the number m. In the example given, y=x^{2} 4x+ 3, the graph is not a line and so doesn't have a slope. One definition of "derivative" is that the derivative, at any given value of x, is the slope of the tangent line.



#6
Sep306, 06:31 PM

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How would you graph this equation w/out plugging in points or using a calculator? 


#7
Sep306, 06:52 PM

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#8
Sep306, 08:12 PM

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b/c i want to know how to graph it



#9
Sep306, 08:26 PM

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#10
Sep406, 02:02 PM

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Well, I think it was in fifth grade where they taught me to make a list of x y values:
x y= x^{2} 4x+ 3 0 3 1 1 4+ 3= 0 1 1+ 4+ 3= 8 2 4 8+ 3= 1 2 4+ 8+ 3= 15 3 9 12+ 3= 0 3 9+ 12+3= 24 etc, mark the points (0,3), (1, 0), (1, 8), (2, 1), (2, 15), (3, 0), (3, 24) and then draw a smooth curve through the points. Another method, that I think I didn't learn until 9th or 10th grade was to complete the square: if y= x^{2} 4x+ 3= x^{2} 4x+ 4 4+ 3= (x 2)^{2} 1. The graph is a parabola with vertex (2, 1) opening upward. 


#11
Sep406, 10:52 PM

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it doesn't hurt to sound stupid sometimes. at least, you are learning something. 


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