HONORS Algebra Two, Polynomial Unit Day 4
Name:________________________ Date: _____________
FINDING THE EQUATIONS OF POLYNOMIALS AND OTHER MIXED PRACTICE
Use each graph to answer the questions and determine the equation of the polynomial.
1.
(a) Is the function even or odd? ____________
(b) Is the leading coefficient positive or negative? __________
y
5
(c) What is the degree of the function? ____________
(d) List the zeros and the multiplicity of each zero:
–2
2
x
4
Zero: _________ with a Multiplicity of: _______
Zero: _________ with a Multiplicity of: _______
–5
(e) What is the factored form of the equation? ___________________
2.
(a) Is the function even or odd? ____________
(b) Is the leading coefficient positive or negative? __________
y
5
(c) What is the degree of the function? ____________
(d) List the zeros and the multiplicity of each zero:
–2
2
4
x
Zero: _________ with a Multiplicity of: _______
Zero: _________ with a Multiplicity of: _______
–5
Zero: _________ with a Multiplicity of: _______
(e) What is the factored form of the equation? _____________________
3.
(a) Is the function even or odd? ____________
y
10
(b) Is the leading coefficient positive or negative? __________
5
(c) What is the degree of the function? ____________
–2
2
–5
–10
4
x
(d) List the zeros and the multiplicity of each zero:
Zero: _________ with a Multiplicity of: _______
Zero: _________ with a Multiplicity of: _______
(e) What is the factored form of the equation? _____________________
Use factoring and/or the quadratic formula to solve (find the zeros of) the following polynomial equations.
4. p( x)  16 x 4  1
5. r ( x)  x3  2 x 2  3x  6
Use factoring and/or the quadratic formula to solve (find the zeros of) the following polynomial equations.
6. g ( x)  x3  2 x 2  3x
7. y( x)  8 x3  27
Graphing Calculator Practice
GRAPH each function and then use the ZERO function on the CALC menu to find the zeros of each function.
Remember, another word for the zeros of the function is ______________________, ________________, or solutions.
Graph each function on your graphing calculator so the complete graph is shown. (You may have to adjust your
window.) Then, approximate each of the real zeros to the nearest hundredth. If there are any imaginary solutions,
identify the number of imaginary solutions.
8. f ( x)  x3  3
(a) What is the degree? ______
(b) What is the number of real solutions? _______
(c) What is the number of imaginary solutions? _______
(d) What are the real solutions? ______________
9. m( x)  3x 4  x 2  x  1
(a) What is the degree? ______
(b) What is the number of real solutions? _______
(c) What is the number of imaginary solutions? _______
(d) What are the real solutions? ______________
10. p( x)  x 4  x 2  6
(a) What is the degree? ______
(b) What is the number of real solutions? _______
(c) What is the number of imaginary solutions? _______
(d) What are the real solutions? ______________
Algebra Two
Name: _______________________ Date: _____________
HOMEWORK - MULTIPLICITY AND ROOTS ON THE GRAPHING CALCULATOR
Use factoring and/or the quadratic formula to solve (find the zeros of) the following polynomial equations.
11. g ( x)  x3  27
12. y ( x)  x 4  16 x 2
Sketch the graphs of the following polynomials given the constraints.
13. Sketch a 4th degree polynomial with a positive leading coefficient, a double root at 2 and 2 imaginary roots.
14. Sketch a 5th degree polynomial with a negative leading coefficient, a root at zero with a multiplicity of one, a root
at negative three with a multiplicity of two and two imaginary roots.
Graph each function on your graphing calculator so the complete graph is shown. (You may have to adjust your
window.) Then, approximate each of the real zeros to the nearest hundredth.
15. f ( x)  x3  1
(a) What is the degree? ______
(b) What is the number of real solutions? _______
16. m( x)  x 4  3x 2  1
(a) What is the degree? ______
(b) What is the number of real solutions? _______
(c) What is the number of imaginary solutions? _______
(c) What is the number of imaginary solutions? ____
(d) What are the real solutions? ______________
(d) What are the real solutions? ______________
17. If a function has a zero at 2 with a multiplicity of 3, then what is the equation (factored form) of the 3rd degree
polynomial?
18. If a function has a zero at 0 with a multiplicity of 2 and a zero at -1, then what is the3rd degree equation (factored
form) of the function?
Given the zeros of the equation, determine the original equation (simplest).
19. Zeros = 0 with a multiplicity of 1 and 2 with a multiplicity of 2
y
5
–2
2
–5
x
20. Zeros =
1
and 3
3
21.(a) Is the function even or odd? _____; (b) Is the leading coefficient positive or negative? ____
(c) What is the degree of the function? ____________
(d) List the zeros and the multiplicity of each zero:
Zero: ______ with a Multiplicity of: ______; Zero: _________ with a Multiplicity of: _______
(e) What is the factored form of the equation? _____________________