Question

graph the polynomial function f(x)=(x - 1)(x + 4)^2 using parts (a) through (e). the y - intercept is - 16. (simplify your answer. type an integer or a fraction.) (c) determine the zeros of the function and their multiplicity. use this information to determine whether the graph crosses or touches the x - axis at each x - intercept. the zero(s) of f is/are . (simplify your answer. type an integer or a fraction. use a comma to separate answers as needed. type each answer only once.)

Explanation:

Step1: Set the function equal to zero

Set \(f(x)=(x - 1)(x + 4)^2=0\).

Step2: Use the zero - product property

If \(ab = 0\), then \(a=0\) or \(b = 0\). So \(x-1=0\) gives \(x = 1\) and \((x + 4)^2=0\) gives \(x=-4\).

Answer:

\(1,-4\)