Help with standard form

Question

I have a poly question for Algebra 2. The problem gives me the root of 4 with multiplicty of 2. The root of 5 with multiplicty of 1. I also get the y-intercept of 160. I need to find the problem in standard form.

Answer 1

y = a(x - 4)²(x - 5) (this gives the right roots with the right multiplicity)

160 = a(-4)²(-5) (we plug in the given y-int coordinates to solve for a, the lead coefficient)

160 = - 80a

a = -2

y = -2(x - 4)²(x - 5)