Question

how do you write an equation in factored form with the y intercept and roots?

Answer 1

if the roots are a,b,c,...
y = k(x-a)(x-b)(x-c)...
where k can be any number. If the y-intercept is Y, then just set x=0 and then
k(-a)(-b)(-c)... = Y
and k = Y/((-a)(-b)(-c)...)

for example, if the roots are -1 and 3, with a y-intercept of 4, then
y = -4/3 (x+1)(x-3)