Answer:
The y-intercept y = -9
Step-by-step explanation:
Given the function
[tex]f\left(x\right)\:=\:\left(x+1\right)\left(x-9\right)\left(x-1\right)^2[/tex]
Determining the y-intercept of the function
We know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.
so substitute x = 0 in the function
[tex]y\:=\:\left(x+1\right)\left(x-9\right)\left(x-1\right)^2[/tex]
[tex]y\:=\:\left(0+1\right)\left(0-9\right)\left(0-1\right)^2[/tex]
[tex]y=1\cdot \left(-9\right)\left(0-1\right)^2[/tex]
[tex]y=1\cdot \left(-9\right)\cdot \:1[/tex]
[tex]y=-1\cdot \:9\cdot \:1[/tex]
[tex]y=-9[/tex]
Therefore, the y-intercept y = -9
