Question

graph the polynomial function f(x)=(x + 1)^2(x - 5)^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^4 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 only once.)

Explanation:

Step1: Find x - intercepts

Set \(f(x)=0\), so \((x + 1)^2(x - 5)^2=0\). Then \(x+1 = 0\) or \(x - 5=0\). Solving \(x+1=0\) gives \(x=-1\), and solving \(x - 5=0\) gives \(x = 5\).

Step2: Find y - intercept

Set \(x = 0\) in \(f(x)\). Then \(f(0)=(0 + 1)^2(0 - 5)^2=1\times25 = 25\).

Answer:

The x - intercept(s) is/are \(-1,5\)