Answer: The graph that could be the graph of f(x) is a parabola that opens upwards, with a vertex at (2,-4) and x-intercepts at x = -1 and x = 4. Since the degree of the polynomial function f(x) is 3 and the roots are -1, 0, and 4, the polynomial function is a cubic function and its graph is a parabola.
The roots of a polynomial function are the x-coordinates of the x-intercepts of the graph of the function. Therefore, since the roots of the equation f(x) = 0 are -1, 0, and 4, the graph of f(x) will have x-intercepts at x = -1 and x = 4.
The fact that the vertex is at (2, -4) mean that the parabola will open upwards and pass through the point (2, -4)
It's important to note that, if the polynomial function has a degree greater than 3, there may be multiple graphs that could represent the polynomial function, as long as they have the same roots.
Explanation: