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For the polynomial function f(x) = -x(x-4)(x+5), answer parts a through e. a. Us

ID: 2910686 • Letter: F

Question

For the polynomial function f(x) = -x(x-4)(x+5), answer parts a through e. a. Use the Leading Coefficient Test to determine the graph's end behavior. O A. The graph of f(x) falls to the left and falls to the right. O B. The graph of f(x) rises to the left and rises to the right. O C. The graph of f(x) rises to the left and falls to the right. 0 D. The graph of f(x) falls to the left and rises to the right. b. Find the x-intercept(s). The x-intercept(s) is/are. (Type an integer or a decimal. Use a comma to separate answers as needed.) At which zero(s) does the graph of the function cross the x-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The graph crosses the x-axis at the zero(s). (Type an integer or a decimal. Use a comma to separate answers as needed.) O B. There are no zeros at which the graph crosses the x-axis. At which zero(s) does the graph of the function touch the x-axis and turn around? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The graph touches the x-axis and turns around at the zero(s). (Type an integer or a decimal. Use a comma to separate answers as needed.) O B. There are no zeros at which the graph touches the x-axis and turns around. c. Find the y-intercept. The y-intercept is. (Simplify your answer.) d. Determine whether the graph has y-axis symmetry, origin symmetry, or neither. Choose the correct answer below. O A. The graph of f is symmetric about the y-axis. O B. The graph of f is symmetric about the origin. OC. The graph of f is neither symmetric about the y-axis nor symmetric about the origin.

Explanation / Answer

f(x) = -x^2 ( x-4) ( x + 5 )

a) leading coefficient - x^4

the graph rises to the left and falls to the right

b) - x^2 ( x- 4) ( x+ 5) = 0

x intercepts are x= 0 , 4 , -5

the graph crosses the x axis at -5 and at x = 4

the graph touches the x axis at x = 0

y intercept = 0, 0

d) the graph has y axis symmetry