Question

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

Answer 1

To find the x-intercepts of f(x) = x³ - 9x² + 20x - 12, set f(x) to zero and divide by (x - 6), then solve the remaining polynomial. To find the y-intercept, evaluate f(0) to get -12.

Step-by-step explanation:

The student asked how to find the x-intercepts and the y-intercept of the function f(x) = x³ - 9x² + 20x - 12, given that (x - 6) is a factor. To find the x-intercepts, we set f(x) to zero and solve for x. Since (x - 6) is a factor, we divide the polynomial by (x - 6) using polynomial long division or synthetic division to find the other factors. After dividing, we obtain the reduced polynomial which we can then factor further or use the quadratic formula to solve for remaining x values that satisfy f(x) = 0.

To find the y-intercept, we evaluate f(x) at x = 0. So, the y-intercept is f(0) which is simply the constant term of the polynomial, in this case, -12.

Step-by-step for finding the x-intercepts:

Step for finding the y-intercept: