Question

f(x) = 3(x-4)^2 (x+4)

what is the left and right hand behavior of this equation?

What is the y intercept?

Answer 1

y intercept = 3* 4^2*4 = 192 (192, 0)
Both left and right raising up

Answer 2

Do you know what the multiplicities of zero would be?

Answer 3

(x-4)^2 will be positive for all real x
(x+4) will be negative for x<-4.
so for large negative x, the entire expression will become a large negative number.
Going left, it tends to negative infinity. (down)
Going right, it tends to positive infinity (up)