Question 423861


Recall that x-intercepts are another name for the roots or zeroes of a polynomial. 

generally a root is termed " even " if it is a root an even number of times...similarly for " odd "

{{{f(x) = ( x+ 5)^4 ( x -6) ^3}}} has {{{-5}}} as an even root and {{{6}}} as an odd root

at "even " roots the graph touches but does not cross the domain axis..." odd " implies crossing

or

If a root has an {{{even}}} multiplicity, the graph will {{{bounce}}}{{{ off}}} the axis, as with the graph of {{{y=x^2}}}. If a root has an {{{odd }}}multiplicity, the graph will {{{pass}}}{{{ through}}} the axis, as with the graph of {{{y=x^3}}}.