Write equation based on graph

Question

Write the equation of a polynomial with the same end-behaviour, x-intercepts, and multiplicities with the graph below. Please explain your answer!

https://imgur.com/a/qpNDcar

Answer 1

looks like 7th degree polynomial:

-8 is a solution of multiplicity 2, -4 is a solution, 1 is a solution, 5 is a solution of multiplicity 2, 7 is a solution

based on the end behavior the leading term must be -x^7

thus far f(x) = -k(x+8)^2(x+4)(x-1)(x-5)^2(x-7)

the y-intercept is (0,-2), so f(0)=-2

-2 = -k(64)(4)(-1)(25)(-7)

k = -1/11200