Answer:
y(x) = (1/9)(x +4)(x +3)(x -1)(x -3)
Step-by-step explanation:
It has roots at -4, -3, 1, and 3 so can be written in the form ...
y(x) = a(x +4)(x +3)(x -1)(x -3)
We can determine at the value of "a" by looking at the y-intercept. Filling in x=0 in the above equation, we get ...
y(0) = 36a
We see on the graph that y(0) = 4, so "a" is ...
4 = 36a
4/36 = 1/9 = a
The polynomial is ...
y(x) = (1/9)(x +4)(x +3)(x -1)(x -3)
