Pre-Calculus WS 2-2: Polynomials
Name:
For each of the following:
a. Find each zero and its multiplicity
b. Determine whether the graph crosses or touches the xaxis at each x-intercept (zero)
c. Determine the maximum number of turning points
d. Determine the end behavior of the graph
1. f ( x)  3( x  7)( x  4) 2
a.
b.
c.
d.
2. f ( x)  4( x  4)( x  3) 3
a.
b.
c.
d.
3. f ( x)  ( x  5) 3 ( x  4) 2
a.
b.
c.
d.
4. f ( x)  2( x  3)( x  4) 3
a.
b.
c.
d.
5. f ( x)  x 2 ( x  2)
a.
b.
c.
d.
For each of the following:
a. Find the zeros (may need to factor) and multiplicity
b. Determine if graph crosses or touches the graph at the
zeros (using multiplicity)
c. Determine the end behavior
d. Find the y-intercept(s)
e. Sketch the graph by hand (no calculators)
6. f ( x)  x 2 ( x  3)
a.
b.
c.
d.
e.
7. f ( x)  ( x  4)( x  2) 2
a.
b.
c.
d.
e.
8. f ( x)  x 3  2 x 2  8x
a.
b.
c.
d.
e.
9. f ( x)  x 3  x 2  12 x
a.
b.
c.
d.
e.