Explanation:
According to the graph, the function has
- 5 roots ⇒ x = - 3, - 2, - 1, 1, 3
- The function is decreasing so the leading term has negative coefficient.
- One of the local maximums is approximately (2, 6)
- The y-intercept is (0, - 1.5)
The coefficient is going to be:
- - 1.5 / (3*2*3) = - 1.5/18 = - 1/12
One possible option is:
- f(x) = - 1/12 (x + 3)(x + 2)(x + 1)(x - 1)(x - 3)
See attached