Question

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.

Answer 1

To find the x-intercepts, set the function equal to zero and solve for x. One of the factors of the function is (x - 6), so x = 6 is an x-intercept. To find the y-intercept, substitute 0 for x in the function and solve for f(0). The y-intercept of the graph is at y = -12.

Step-by-step explanation:

To find the x-intercepts of the graph of the function f(x), we need to set the function equal to zero and solve for x. Since one factor of the function is (x-6), we can set it equal to zero:

(x-6) = 0

Solving for x, we get x = 6. So, the x-intercept of the graph is at x = 6.

To find the y-intercept of the graph, we need to substitute 0 for x in the function and solve for f(0). Plugging in x = 0 in the function f(x), we get:

f(0) = (0³ - 9(0)² + 20(0) - 12)

Calculating further, we find f(0) = -12. Therefore, the y-intercept of the graph is at y = -12.