Hi,

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

Note that below is question 1:

I was easily able to develop the equation for question 1, which the question prompt for a linear equation, as follows:

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:

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

Help would be greatly appreciated.

2. ## 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 ...