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Thread: Creating equation from graph

  1. #1
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    Question Creating equation from graph

    Hi,

    I hope someone can help. I'm trying to understand how a given equation matches the following function characteristics:
    Creating equation from graph-screen-shot-2017-04-08-8.42.39-pm.png

    The equations are:
    Creating equation from graph-screen-shot-2017-04-08-8.44.55-pm.png

    I understand that the function needs to have an odd degree, one zero at x = 2 that has a multiplicity of 2 (in order for it to "bounce back" and cross y = 2 when x = 0), and another zero at x = -1. However, I don't understand how to get to the textbook's example equation's above. Please help!

    Best,
    Olivia
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  2. #2
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    Re: Creating equation from graph



    I plotted the four given points and started with $f(x) = k(x+1)^2(x-3)$

    since $f(-3) = 16$ ...

    $16 = k(-3+1)^2(-3-3)$

    $16 = -24k \implies k = -\dfrac{2}{3}$

    $f(x) = -\dfrac{2}{3}(x+1)^2(x-3)$
    Attached Thumbnails Attached Thumbnails Creating equation from graph-neg_cubic.jpg  
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