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 December 11th, 2012, 05:58 PM #1 Newbie   Joined: Dec 2012 Posts: 8 Thanks: 0 Vector question I have a question and I think it isnt that hard but it has been eons since I have seen a vector question. Any help would be appreciated. The graph of f(x) = 3x^3-2x^2+x+2 is translated to its image g(x) by the vector (1 over -2) Write the equation of g(x) in the form g(x) =ax^3+bx^2+cx+d Any help would be reeeeeaaall;;y appreciated. THANKS!
December 11th, 2012, 09:20 PM   #2
Math Team

Joined: Dec 2006
From: Lexington, MA

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Re: Vector question

Hello, coachcft!

I'm not sure what your "vector translation" means.

Quote:
 The graph of $f(x) \:=\: 3x^3\,-\,2x^2\,+\,x\,+\,2$ is translated to its image $g(x)$ by the vector (1 over -2). Write the equation of $g(x)$ in the form $g(x)\:=\:ax^3\,+\,bx^2\,+\,cx\,+\,d$

I'll assume that the vector translation moves the graph [color=blue]1 unit to the right[/color] and [color=blue]2 units down[/color].

$\text{If that's true, we have: }\:g(x)\,-\,(-2) \;=\;3(x\,-\,1)^3\,-\,2(x\,-\,1)^2\,+\,(x\,-\,1)\,+\,2$

$\text{Simplify and solve for }g(x).$

 December 12th, 2012, 03:40 AM #3 Newbie   Joined: Dec 2012 Posts: 8 Thanks: 0 Re: Vector question That was very helpful, thank you so much!

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