Using the provided data, we wish to graph a polynomial.
The given information describes a polynomial with specific characteristics.
A polynomial with one minimum and one maximum suggests it's at least a cubic function, as it has two turning points.
The presence of three zeros indicates a cubic polynomial, as the number of zeros corresponds to the degree of the polynomial.
Given that (x - 4) is a factor, it implies that x = 4 is one of the zeros.
Therefore, the other two zeros must come from different factors.
This polynomial may be factored as
(x−4)(x−a)(x−b), where a and b are the other zeros.
The general graph would depict a cubic function with a relative minimum on the left, a relative maximum on the right, and three x-intercepts.
The relative minimum occurs where the polynomial changes direction from decreasing to increasing, and the relative maximum occurs where it changes from increasing to decreasing.
The zero at x = 4 suggests that the graph touches or crosses the x-axis at this point.
The specific values of a and b would determine the exact shape of the graph and the locations of the minimum, maximum, and zeros.