Question

Given a cubic function, f(x), with a leading coefficient of -1 and the following zeros: x = 0, x = 2, x = -1.

a) Write this polynomial function in factored form.
b) Sketch a rough graph of f(x) showing correct zeros and end behavior.
c) Give the coordinates for the y-intercept.
Show Your Work

Answer 1

The factored form of the cubic function is f(x) = -1(x-0)(x-2)(x+1). The graph of f(x) will have zeros at x=0, x=2, and x=-1 and a downward slope for its end behavior. The y-intercept of the graph is at the point (0,0).

Step-by-step explanation:

a) The factored form of the cubic function with zeros at x=0, x=2, and x=-1 is f(x) = -1(x-0)(x-2)(x+1).

b) To sketch a rough graph of f(x), plot the zeros at x=0, x=2, and x=-1 on the x-axis. Since the leading coefficient is -1, the end behavior of the graph will be a downward slope on both sides of the graph.

c) The y-intercept occurs when x=0. Substituting this value into the factored form of the function, we get f(0) = -1(0-0)(0-2)(0+1) = 0. Therefore, the coordinates for the y-intercept are (0,0).