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Solve By Factoring, and Equation of Cubic Function whose graph passes thru

  1. Oct 20, 2008 #1
    1. The problem statement, all variables and given/known data


    I am stuck on these two pre-cal problems... can anyone help?

    Solve By Factoring: 2x^3 + 2x^2 = 4x + 4

    This next one I have no idea how to do

    Find an equation of the cubic function whose graph passes through the points (3,0) and (1,4) and is tangent to the x-axis at the origin...
     
  2. jcsd
  3. Oct 20, 2008 #2
    Try putting all the terms on one side so that they all equal 0.
     
  4. Oct 20, 2008 #3
    alrite I think I am ok with the first problem, but I'm still stuck on the second one...
     
  5. Oct 20, 2008 #4
    What can you tell from the point (3,0)?

    EDIT: And what can you say since the line passes through the origin?
     
  6. Oct 21, 2008 #5

    HallsofIvy

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    You need to find a, b, c, and d of y= ax3+ bx2+ cx+ d so that
    a) when x= 3, y= 0
    b) when x= 1, y= 4
    c) when x= 0, y= 0 and y'= 3ax2+ 2b2+ c= 0.

    Putting those values in the equation gives you four linear equations for a,b,c, and d.
     
  7. Oct 21, 2008 #6
    Alright, I think i have it...

    It is x^2 because there is a tangent on the x axis at (0,0), and the other zero is (x-3)

    Through a bit of trial and error I have come to: -2x^2(x-3) and I am pretty sure that works just fine.


    Thanks again everyone who helped you guys are great! :smile:
     
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