Question 1013092
Find the zeros for the given polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around at each zero.

{{{f(x)=x^3 -12x^2+36x}}}....set {{{f(x)=0}}}

{{{x^3 -12x^2+36x=0}}}

{{{x(x^2 -12x+36)=0}}}

{{{x(x^2 -12x+6^2)=0}}}

{{{x(x-6)^2  = 0}}}

The zeros are:
{{{x = 0}}}
The multiplicity at the leftmost zero is: {{{1}}}

{{{(x-6)^2  = 0}}}=>{{{x-6  = 0}}}=>{{{x=6}}}

The multiplicity at the rightmost zero is: {{{2}}}

{{{ graph( 600, 600, -5,15, -10, 10, x^3 -12x^2+36x) }}} 

Does the graph (on the leftmost zero) cross the x-axis or touch the x-axis and turn around:
the graph cross the x-axis

Does the graph (on the rightmost zero) cross the x-axis or touch the x-axis and turn around: 

the graph touch the x-axis and turn around