Find the zeros for the polynomial function and give the multiplicity for each zero

Question

f(x)= 4(x^2)(x+6)^2- State whether the graph crosses the x-axis or touches the x-axis and turns around

Answer 1

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.