# Thread: Creating equation from graph

1. ## Creating equation from graph

Hi,

I hope someone can help. I'm trying to understand how a given equation matches the following function characteristics:

The equations are:

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

2. ## Re: Creating equation from graph

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

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

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

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

$f(x) = -\dfrac{2}{3}(x+1)^2(x-3)$