Question

Find a fifth degree polynomial function that has a bounce point at 5, a pass-through point at 8, additional roots at 8-3i and 8+3i, and a y-intercept at the point (0,7).

Answer 1

what is a bounce point?

Answer 2

ax^5 + bx^4 + cx^3 + dx^2 + ex + f = y

when x=0, f=7 so we have 5 more coefficients to determine using the stated zeros

Answer 3

its a simple thing for a program like wolfram to work a matrix setup on this

Answer 4

well thats not working out as i would have hoped ... lets just work the roots then scale it to meet the y intercept

Answer 5

P(x)=(5-x)(5-x)(8-x)(8-3i-x)(8+3i-x)

http://www.wolframalpha.com/input/?i=y%3D%285-x%29%285-x%29%288-x%29%288-3i-x%29%288%2B3i-x%29

now we scale it by some k such that when x=0, y=7

7
----------------- = k
(5)(5)(8)(8-3i)(8+3i)