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 and turns around at each zero. f(x)=

Algebra ->  Graphs -> 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 and turns around at each zero. f(x)=      Log On


   



Question 1013835: 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 and turns around at each zero.
f(x)=x^3 -6x^2 +9x
a. The zeros are:
b. The multiplicity at the leftmost zero is:
(type a whole number)
c. The multiplicity at the rightmost zero is:
(type a whole number)
d. Determine whether the graph crosses the x-axis or touches the x-axis and turns around at the leftmost zero
e. Determine whether the graph crosses the x-axis or touches the x-axis and turns around at the rightmost zero
My answers:
a. 0,3
b.0
c.3
d.crosses the x-axis
e.crosses the x-axis

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!



answers:
a. 0,3 -> correct
b.0 -> correct
c.3-> incorrect:factored form of given equation is x+%28x-3%29%5E2=x+%28x-3%29%28x-3%29;so,the multiplicity at the rightmost zero is 2 (you have two times %28x-3%29 in factored form)
d.at the leftmost zero the graph crosses the x-axis-> correct
e.at the leftmost zero the graph crosses the x-axis-> incorrect
at the leftmost zero the graph touches the x-axis and turns around at the rightmost zero

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3+-6x%5E2+%2B9x%29+