One factor of the function f(x) = x3 − 9x2 + 20x − 12 is (x − 6). Describe how to find the x-intercepts and the y-intercept of the graph of f(x) without using technology. Show your work and include all intercepts in your answer.

The x-intercepts are:

(1, 0)

(2, 0)

(6, 0)

The y-intercept is (-12, 0)

Step-by-step explanation:

Given the function

Determining the x-intercepts and the y-intercept of the graph of f(x)

Finding x-intercept

We can determine the x-intercept by setting y = 0 and determining the corresponding value of x.

plug in x = 0

as

so

Using the zero factor principle

if ab = 0 then a=0 or b=0 (or both a=0 and b=0)

Thus,

 or    or  

Thus, the x-intercepts are:

(1, 0)

(2, 0)

(6, 0)

Finding y-intercept

We can determine the y-intercept by setting x = 0 and determining the corresponding value of y.

plug in y = 0

Therefore, the y-intercept is (-12, 0)

I apologize if this is incorrect, but I hope this helps! Have a great Monday!

unless if u could do my questions, if not i wouldn't want to

step-by-step explanation: