Question

the volume of the prism is modeled by function v
v(x) = x³ - 12x² + 35x
use the x-intercepts to write the factored form of the equation representing the volume of the prism.
v(x) =

Explanation:

Step1: Identify x-intercepts from graph

The x-intercepts are $x=0$, $x=5$, $x=7$.

Step2: Write factored form template

For roots $r_1, r_2, r_3$, $v(x)=ax(x-r_2)(x-r_3)$

Step3: Solve for leading coefficient $a$

Use original polynomial's leading term $x^3$, so $a=1$.

Answer:

$v(x)=x(x-5)(x-7)$