f(x) = 4(x^2)(x+6)^2
Find the zeroes: x = 0, multiplicity 2, x = -6, multiplicity 2
Does the graph cross the x-axis?
No. Each part- 4, x^2, and (x+6)^2- can never be negative, so f(x) can never be negative.
Does the graph touch the x-axis and turn around?
In other words, does f(x) ever equal zero (without becoming negative)?
Yes. At x = 0 and x = -6.