SOLUTION: Please help me with the problem below: Write the equations of two fourth degree polynomial functions whose graphs pass through the points (-4,0), (-1,0), (0,5), and (5,0).

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me with the problem below: Write the equations of two fourth degree polynomial functions whose graphs pass through the points (-4,0), (-1,0), (0,5), and (5,0).      Log On


   

Question 983489: Please help me with the problem below:
Write the equations of two fourth degree polynomial functions whose graphs pass through the points (-4,0), (-1,0), (0,5), and (5,0).
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%28x%2B4%29%28x%2B1%29%28x-5%29%28x-a%29
This satisfies the three zeros.
(-4,0)
(-1,0)
(5,0)
Now solve for a.
f%280%29=%280%2B4%29%280%2B1%29%280-5%29%280-a%29=5
4%281%29%28-5%29%28-a%29=5
4a=1
a=1%2F4
.
.
.
f%28x%29=%28x%2B4%29%28x%2B1%29%28x-5%29%28x-1%2F4%29
.
.
.
.
.
.
.
You can also multiply by any constant to get another function.
.
.
g%28x%29=5%28x%2B4%29%28x%2B1%29%28x-5%29%28x-1%2F4%29
.
.
.