Question

graph the polynomial function f(x)=(x - 1)(x + 4)^2 using parts (a) through (e). (a) determine the end behavior of the graph of the function. the graph of f behaves like y = x^3 for large values of |x|. (b) find the x - and y - intercepts of the graph of the function. the x - intercept(s) 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: Find x - intercepts

Set $f(x)=0$, so $(x - 1)(x + 4)^2=0$.
Using the zero - product property, if $ab = 0$, then $a = 0$ or $b = 0$.
For $x-1=0$, we get $x = 1$.
For $(x + 4)^2=0$, we get $x=-4$.

Step2: Find y - intercept

Set $x = 0$ in $f(x)$. Then $f(0)=(0 - 1)(0 + 4)^2=(-1)\times16=-16$.

Answer:

The x - intercept(s) is/are $1,-4$.