Question

question #5 the graph of the polynomial f(x)=x³ - 5x² + 2x + 8 is shown below. determine the x - intercepts of f(x)

Explanation:

Step1: Recall x - intercept definition

The x - intercepts of a function \(y = f(x)\) are the values of \(x\) for which \(y = 0\), i.e., the points where the graph of the function crosses the x - axis.

Step2: Identify points on graph

By looking at the graph of \(y=x^{3}-5x^{2}+2x + 8\), we can see that the graph crosses the x - axis at \(x=-1\), \(x = 2\), and \(x = 4\). The x - intercepts are written as the ordered pairs \((-1,0)\), \((2,0)\), and \((4,0)\).

Answer:

\((-1,0),(2,0),(4,0)\)