Using the Factor Theorem, it is found that the function is given by:
[tex]f(x) = 0.0409(x^3 + x^2 - 77x - 330)[/tex]
The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
- In which a is the leading coefficient.
From the graph, the zeroes are [tex]x_1 = -8, x_2 = -3, x_3 = 10[/tex], hence:
[tex]f(x) = a(x + 8)(x + 3)(x - 10)[/tex]
[tex]f(x) = a(x^2 + 11x + 33)(x - 10)[/tex]
[tex]f(x) = a(x^3 + x^2 - 77x - 330)[/tex]
From the y-intercept, that is, when [tex]x = 0, y = -13.5[/tex], we find a.
[tex]f(x) = a(x^3 + x^2 - 77x - 330)[/tex]
[tex]-330a = -13.5[/tex]
[tex]330a = 13.5[/tex]
[tex]a = \frac{13.5}{330}[/tex]
[tex]a = 0.0409[/tex]
Hence:
[tex]f(x) = 0.0409(x^3 + x^2 - 77x - 330)[/tex]
To learn more about the Factor Theorem, you can take a look at https://brainly.com/question/24380382
