Analyze the polynomial function ​f(x)=x^2(x-6) using parts​ (a) through​ (e). Question content area bottom Find the​ x- and​ y-intercepts of the graph of the function.The​ x-intercept(s) is/are

Answer 1

The x-intercepts are the values of x for which the function equals zero. Setting f(x) = x^2(x-6) = 0, we find the x-intercepts by solving the equation:

x^2(x-6) = 0

This equation is satisfied when either x^2 = 0 or x-6 = 0.

For x^2 = 0, the only solution is x = 0.
For x-6 = 0, the solution is x = 6.

Therefore, the x-intercepts are at x = 0 and x = 6.

To find the y-intercept, we plug in x = 0 into the function:

f(0) = 0^2(0-6) = 0

Therefore, the y-intercept is at y = 0.

So, the x-intercepts are at x = 0 and x = 6, and the y-intercept is at y = 0.