Question

question #10 the graph of the polynomial f(x)=x^{3}-5x^{2}+2x + 8 is shown below. determine the y - intercept of f(x). (8,0) (-8,0) (0,8) (0,-8)

Explanation:

Step1: Recall y - intercept formula

The y - intercept of a function \(y = f(x)\) is found by setting \(x = 0\).

Step2: Substitute \(x = 0\) into the function

Given \(f(x)=x^{3}-5x^{2}+2x + 8\), when \(x = 0\), we have \(f(0)=0^{3}-5\times0^{2}+2\times0 + 8\).

Step3: Simplify the expression

\(f(0)=8\). In coordinate - form, the y - intercept is the point \((0,8)\) since at the y - intercept \(x = 0\) and \(y=f(0)\).

Answer:

\((0,8)\)