Why do polynomial terms with an even exponent bounce off the x-axis? Like if it's $f(x) = (x-5)^2(x+6)$
Why, at $x=5$, does the graph reflect off the x-axis?

Normally, at $x=k$ where $f(x)=(x-k)...$ k is where the value of $(x-k)$ changes from a positive to a negative or vice-versa. This changes the entire function because that sign change changes the sign of the entire function. When $(x-k)^2$ crosses k, it retains its sign because of the squared, because any number squared is positive, which means that $(x-k)$ changing signs is irrelevant to total function sign change.
