Graph x^2-4x+3

  1. Graph x^2-4x+3.

    My question:

    1) is -4x a slope?

    I'm trying to graph this equation w/out using a calculator or plugging in points.

  2. jcsd
  3. Hurkyl

    Hurkyl 15,987
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    Do you know what kind of shape the graph has?
  4. Yes, a parabola.
  5. shmoe

    shmoe 1,994
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    You might try completing the square, this should make it clear how it relates to the graph of the good old y=x^2.
  6. HallsofIvy

    HallsofIvy 41,265
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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=x2- 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.

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

    CRGreathouse 3,497
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    Why would you want to graph it?
  9. b/c i want to know how to graph it :smile:
  10. You know that it looks like a parabola. Are you familiar with the vertex form of the equation for a parabola? If so then doing what shmoe suggested would help you graph it.
  11. HallsofIvy

    HallsofIvy 41,265
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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= x2- 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= x2- 4x+ 3= x2- 4x+ 4- 4+ 3= (x- 2)2- 1. The graph is a parabola with vertex (2, -1) opening upward.
  12. i was looking through my math book, and it showed me how to graph it.

    it doesn't hurt to sound stupid sometimes. at least, you are learning something.
    Last edited: Sep 4, 2006
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