Which of these equations has a graph that is tangent to the x-axis at one of its intercepts? Choose all the polynomials that have this property.

y = x^2 + 6x + 9

y = - x^3

y = (x + 2) (x + 6) ^2

y = (x - 5) (x + 3) (x + 1) (x - 5)

y = x^4

An equation is tangent to the x-axis when it has an even number of a certain root. A root is a value of x that results to a value of y = 0.

The first equation has roots - 3, and - 3. The graph will be tangent to the x-axis along with third, the fourth, and the fifth equation by the same condition that they have roots with even multiplicity (repeated in an even number of ways).