SOLUTION: 4.2 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

Algebra ->  Functions -> SOLUTION: 4.2 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      Log On


   

Question 1013092: 4.2
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
The zeros are:
The multiplicity at the leftmost zero is:
The multiplicity at the rightmost zero is:
Does the graph (on the leftmost zero) cross the x-axis or touch the x-axis and turn around:
Does the graph (on the rightmost zero) cross the x-axis or touch the x-axis and turn around:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
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%28x%29=x%5E3+-12x%5E2%2B36x....set f%28x%29=0
x%5E3+-12x%5E2%2B36x=0
x%28x%5E2+-12x%2B36%29=0
x%28x%5E2+-12x%2B6%5E2%29=0
x%28x-6%29%5E2++=+0
The zeros are:
x+=+0
The multiplicity at the leftmost zero is: 1
%28x-6%29%5E2++=+0=>x-6++=+0=>x=6
The multiplicity at the rightmost zero is: 2
+graph%28+600%2C+600%2C+-5%2C15%2C+-10%2C+10%2C+x%5E3+-12x%5E2%2B36x%29+
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