Given:
There are given the polynomial equation:
[tex]f(x)=(x-2)(x+2)^3(x+6)[/tex]Now,
We need to find the value for the x-intercept, y-intercept, maximum, end behaviors, and multiplicity.
So,
First, find the x-intercept and y-intercept:
To find the x-intercept put 0 for y and to find the y-intercept 0 for x.
Then,
The x-intercept and y-intercept are shown below:
[tex]\begin{gathered} f(x)=(x-2)(x+2)^{3}(x+6) \\ x-intercept:(2,0),(-2,0),(-6,0) \\ y-intercept:(0,-96) \end{gathered}[/tex]Now,
The value of maximum and minimum, end behavior and multiplicity is shown below:
[tex]\begin{gathered} End\text{ behaviour: falls to the left and rise to the right} \\ Multiplicity:1,3,1 \end{gathered}[/tex]Final answer:
Hence, the value of x-intercept, y-intercept, end behaviour and multiplicity are shown below:
[tex]\begin{gathered} x-\imaginaryI ntercept:(2,0),(-2,0),(-6,0) \\ y-intercept:(0,-96) \\ End\text{behav}\imaginaryI\text{our: falls to the left and rise to the right} \\ Mult\imaginaryI pl\imaginaryI c\imaginaryI ty:1,3,1 \end{gathered}[/tex]