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?

Well... at $x=5$, it is clear that 
$$f(5)=(5-5)^2(5+6)=0^2*11=0$$
So from here, you need to observe that if you pick some number greater than $5$ for $x$ (we can write this as $x=5+x_0$, where $x_0 >0$) then we get 
$$f(5+x_0) = ((5+x_0)-5)^2((5+x_0)+6)=(x_0)^2(11+x_0)>0$$
The $>$ above is true because $(x_0)^2$ is always positive and $11+ x_0$ is positive because $x_0>0$. But this is true for any $x_0 >0$ and it only gets bigger for larger $x_0$, so this is why it looks the way it does.
