Polynomial Review Task for Unit 3 for Algebra 2
I. Explore the graph of the polynomial function f ( x)  2 x 3  5 x 2  14 x  8
A. Classification
1. Classify this polynomial by degree: _________________
2. State the number of terms it has: _________________
B. Symmetry
1. Is the function symmetric about the y-axis? ________________
2. Is the function symmetric about the origin? _________________
3. Is the function even, odd, or neither? _________________
C. Domain and Range
1. State the domain of the function: _________________
2. State the range of the function: _________________
D. X-Intercepts, Factors, and Zeros
1. Identify all the x-intercepts of the graph of the polynomial function: _________________
2. Identify all the factors of the polynomial function: _________________
3. Identify all the zeros or roots of the polynomial function: _________________
4. How many zeros does the function have? _________________
E. End-Behaviors
1. Describe the left end-behavior of the graph of this function: _________________
2. Describe the right end-behavior of the graph of this function: _________________
F. Relative Maximums and Minimums
1. Identify all of the relative minimum(s) in the graph of the polynomial function: _____________
2. Identify all of the relative maximum(s) in the graph of the polynomial function: _____________
G. Intervals of Increase or Decrease
1. Identify all of the intervals of increase in the graph of the polynomial function: _____________
2. Identify all of the intervals of decrease in the graph of the polynomial function: _____________
II. Explore the graph of the polynomial function f ( x)  x 4  5 x 3  5x 2  5x  6
H. Classification
1. Classify this polynomial by degree: _________________
2. State the number of terms it has: _________________
I. Symmetry
1. Is the function symmetric about the y-axis? ________________
2. Is the function symmetric about the origin? _________________
3. Is the function even, odd, or neither? _________________
J. Domain and Range
1. State the domain of the function: _________________
2. State the range of the function: _________________
K. X-Intercepts, Factors, and Zeros
1. Identify all the x-intercepts of the graph of the polynomial function: _________________
2. Identify all the factors of the polynomial function: _________________
3. Identify all the zeros or roots of the polynomial function: _________________
4. How many zeros does the function have? _________________
L. End-Behaviors
1. Describe the left end-behavior of the graph of this function: _________________
2. Describe the right end-behavior of the graph of this function: _________________
M. Relative Maximums and Minimums
1. Identify all of the relative minimum(s) in the graph of the polynomial function: _____________
2. Identify all of the relative maximum(s) in the graph of the polynomial function: _____________
N. Intervals of Increase or Decrease
1. Identify all of the intervals of increase in the graph of the polynomial function: _____________
2. Identify all of the intervals of decrease in the graph of the polynomial function: _____________
III. Problem Solving and Applications
A. From 1985 to 1995, the number of nursing schools in the United States could be modeled by
f (t )  0.036t 4  0.605t 3  1.87t 2  4.67t  82.5 where f(t) is the number of graduates, in thousands, and t is
the number of years since 1985.
1. Describe the right end-behavior of the graph of this function: _____________________________
2. Would you expect the number of nursing graduates in 2010 to be more or less than in 1995? Why?
______________________________________________________________________________
3. Find the first year when the number of nursing graduates is over 90,000. ___________________
B. The producer price index of butter from 1991 to 1999 can be modeled by the function
P( x)  0.233x 4  2.64 x 3  6.59 x 2  3.93x  69.1 where x is the number of years since 1991
1. Identify any turning points on the graph in the interval 0  x  8 . _________________________
2. What real-life meaning do these points have? __________________________________________
_______________________________________________________________________________
C. Construct a polynomial having the following characteristics: third degree, negative leading coefficient,
and three real zeros. Sketch the graph of your polynomial below and label the x-intercepts and all turning
points on the graph.