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Thread: Quadratic word problem

  1. #1
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    Question Quadratic word problem

    Hi,

    I hope someone can help me determine the quadratic equation for the following word problem:

    Quadratic word problem-screen-shot-2017-06-29-8.01.48-pm.png


    Note that below is question 1:
    Quadratic word problem-screen-shot-2017-06-29-8.02.45-pm.png


    I was easily able to develop the equation for question 1, which the question prompt for a linear equation, as follows:
    Quadratic word problem-screen-shot-2017-06-29-8.05.18-pm.png

    Now for question 2, I need to develop a quadratic equation which represents the pool being drained. I know that the vertex would be at (8,0) and that the quadratic equation format is y = a(x-h)^2+k, but I don't know where to go from there in terms of developing the equation for word problem. According to the textbook the equation is:

    Quadratic word problem-screen-shot-2017-06-29-8.07.58-pm.png

    I understand the (x-8)^2 part, but not the value for "a", as in (6.35\pi)/64

    Help would be greatly appreciated.
    Last edited by otownsend; Jun 29th 2017 at 05:13 PM.
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  2. #2
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    Re: Quadratic word problem





    initial volume, $V_0 = \pi\left(\dfrac{5}{2}\right)^2 \cdot 1 = \dfrac{25\pi}{4} \, m^3$

    two points on the quadratic curve $(t,V)$

    $\left(0, \dfrac{25\pi}{4}\right)$ and $(8,0)$

    $V = a(t-8)^2$

    $\dfrac{25\pi}{4} = a(0-8)^2 \implies a = \dfrac{25\pi}{4 \cdot 64}$

    which leads to the equation you posted ...

    Thanks from otownsend
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