For the graph shown below do the following a Find the zeros

For the graph shown below do the following. a. Find the zeros and state the multiplicity of each zero. b. Write an equation, expressed as the product of factors, of a polynomial function for the graph. Use a leading coefficient of 1 or - 1 and make the degree of f as small as possible. c. Use both the equation in part (b) and the graph to find the y-intercept a. List the zeros whose multiplicity is even. Select the correct choice below and fill in any answer boxes within your choice. A. B. There are no such zeros. List the zeros whose multiplicity is odd. Select the correct choice below and fill in any answer boxes within your choice. A. B. There are no such zeros. b. Write an equation, expressed as the product of factors, of a polynomial function for the graph. Use a leading coefficient of 1 or - 1 and make the degree of f as small as possible. f(x) = c. The y-intercept is

Solution

a. The zeros whose multiplicity is even are 0, 2. (multiplicity 2 each)The zero whose multiplicity is odd is -1 (multiplicity 1)

b. The graph of the function is not symmetric about the Y-Axis. Therefore, the function is not even. Further, the zeros of the function being 0, 2   (of multiplicity 2 each) and -1 (multiplicity 1), the function of least degree which meets all the above observations, with a leading coefficient 1 or, -1 is    f(x) = ± x² (x -2)² (x+1)

c. The y-intercept of the function is where x = 0. Thus, the y-intercept is 0.