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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? __________

(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? ___________________

2. (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: _______

Zero: _________ with a Multiplicity of: _______

(e) What is the factored form of the equation? _____________________

3.

(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? _____________________

Use factoring and/or the quadratic formula to solve (find the zeros of) the following polynomial equations.

4. [pic] 5. [pic]

Use factoring and/or the quadratic formula to solve (find the zeros of) the following polynomial equations.

6. [pic] 7. [pic]

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. [pic]

(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. [pic]

(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. [pic]

(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 A.17 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. [pic] 12. [pic]

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. [pic] 16. [pic]

(a) What is the degree? ______ (a) What is the degree? ______

(b) What is the number of real solutions? _______ (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 20. Zeros = [pic] and 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? _____________________

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