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?

The expanded form of the polynomial is a cubic with leading coefficient of $1$.  Hence, $\displaystyle \lim_{x \rightarrow \infty} f(x) = \infty$ and $\displaystyle \lim_{x \rightarrow -\infty} f(x) = -\infty$.
The polynomial has only two zeros: $x = 5$ and $x= -6$.  It cannot touch the $x$-axis anywhere else.
Once you begin sketching the graph, it should become obvious why the graph must "bounce" off the $x$-axis at $x = 5$.  
You should be able to generalize the idea from here.  :)
