Final answer:
The polynomial function f(x), use the given degree, y-intercept, and roots is f(x) = a(x + 3)(x - 4)(x + 1)^2.
Step-by-step explanation:
The polynomial function f(x) can be determined using the given information:
- degree 4
- y-intercept of -24
- roots of -3 and 4
- multiplicity 2 root of -1
Since the degree of the polynomial is 4, it will have 4 terms.
The y-intercept can be represented by the constant term.
The roots are the values that make the polynomial equal to zero.
The multiplicity of a root represents how many times it appears as a solution.
Therefore, f(x) can be written as: f(x) = a(x + 3)(x - 4)(x + 1)^2, where 'a' represents a constant coefficient of the polynomial.