Download 6.2 Graphing Polynomial Functions in Factored Form WS.

Algebra 2 Pre-AP
Unit 3. Module 6.
Name: ________________________
6.2 Graphing Polynomial Functions in Factored Form
1. y  ( x  1)( x  2)( x  3)
From what we know about functions, if we set the expression equal to 0, where would you
expect this function to cross the x-axis?
Now multiply it out and see the function in standard form.
Is the graph going to be quadratic? Why or why not?
Graph the function with the calculator.
2.
f ( x)  ( x  3)( x  2)( x  1)
Follow the same steps as number 1.
Where do you expect the function to cross the x-axis?
Multiply it out and write in standard form.
Is the graph going to be quadratic? Why or why not?
Graph the function with the calculator.
3. When the functions are written in standard form, what is the degree of the function in
questions 1 and 2? What is similar about the 2 graphs? What is different about the 2
graphs? What do you think caused this to happen?
4.
f ( x)  x3 (2  x)
Follow the same steps as number 1.
Where do you expect the function to cross the x-axis?
Multiply it out and write in standard form.
Is the graph going to be quadratic? Why or why not?
Graph the function with the calculator.
5. y  ( x  1)( x  2)( x  2)( x 1)
Follow the same steps as number 1.
Where do you expect the function to cross the x-axis?
Multiply it out and write in standard form.
Is the graph going to be quadratic? Why or why not?
Graph the function with the calculator.
6. When the functions are written in standard form, what is the degree of the function in
questions 4 and 5? What is similar about the 2 graphs? What is different about the 2
graphs? What do you think caused this to happen?
7. Odd degree polynomial functions begin and end in (circle one) same/opposite directions.
Even degree polynomial functions begin and end in (circle one) same/opposite directions.
Sketch the following polynomials on the axis provided. Find all the zeros for each polynomial,
indicate any multiplicities other than 1, and determine end behavior.
8. g ( x)  ( x  3)( x  2)( x  1)
LC positive/negative ________________
Odd/even _________________________
Zeros _____________________________
Multiplicity _________________________
End behavior
_________________
_________________________________
Degree ____________________________
# of turning points __________________
9. h( x)   x( x  2)( x  4)( x  1)
LC positive/negative ________________
Odd/even __________________________
Zeros _____________________________
Multiplicity _________________________
End behavior _______________________
_________________________________
Degree ____________________________
# of turning points ___________________
10. p( x)  ( x  2) 2 ( x  3)
LC positive/negative ________________
Odd/even __________________________
Zeros ______________________________
Multiplicity _________________________
End behavior _______________________
_________________________________
Degree _____________________________
# of turning points ____________________
11. p( x)  ( x  1)2 ( x  2)
LC positive/negative ________________
Odd/even __________________________
Zeros ______________________________
Multiplicity _________________________
End behavior _______________________
_________________________________
Degree _____________________________
# of turning points ____________________
12. j ( x)  3( x  1)3 x 2
LC positive/negative ________________
Odd/even __________________________
Zeros ______________________________
Multiplicity _________________________
End behavior _______________________
_________________________________
Degree _____________________________
# of turning points ____________________
13. f ( x)  ( x  3)5 ( x  1)
LC positive/negative ________________
Odd/even __________________________
Zeros _____________________________
Multiplicity _________________________
End behavior _______________________
_________________________________
Degree ____________________________
# of turning points ___________________