Download Algebra 2 Unit 3 Notebook Guide

Name:________________________
Algebra 2
Unit 3
Notebook Guide
Unit Topic: Polynomials and Polynomial Functions (Chapter 5)
Date
Lesson
Textbook Section Homework Assignment
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1. Use Properties of Exponents
5.1 HW #1 (p. 333) 17, 19, 21, 23, 25, 27, 31, 35, [47]
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2. Evaluate and Graph Polynomial Functions
5.2 HW #2 (p. 341) 5, 7, 9, 11, 19, 21, 31, 35, 43, 49
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3. Add, Subtract, and Multiply Polynomials
5.3 HW #3 (p. 349) 3, 5, 7, 11, 17, 19, 25, 29, 39, 43
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4. Factor and Solve Polynomial Equations
5.4 HW #4 (p. 356) 3, 7, 11, 15, 19, 23, 33, 39, [55, 57]
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5. Apply the Remainder and Factor Theorem
5.5 HW #5 (p. 366) 5, 17, 21, 23, 25, 27, 29, 31, [37]
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6. Skills Review
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7. Find Rational Zeros
5.6 HW #7 (p. 374) 3, 5, 11, 13, 25, 27, [19, 21]
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8. Apply the Fundamental Theorem of Algebra
5.7 HW #8 (p. 383) 15, 17, 23, 31, 37, 41, 45, 49, [57]
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9. Analyze Graphs of Polynomial Functions
5.8 HW #9 (p. 390) 3, 9, 15, 19, 25, 27, [35, 37]
HW #6 (p. 407) 1, 2, 3, 4, 6, 7, 9, 10, 12, 13, 14, 15, 16, 27
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10. Write Polynomial Functions and Models
5.9 HW #10 (p. 397) 3, 5, 7, 9, 15, 17, 19, 21, [29]
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11. Skills Review
HW #11 (p. 407) 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29
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12. Unit 3 Review
Unit 3 Review
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13. Problem Solving
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14. Unit 3 Test
5.1-5.9 Problem Solving (p. 369) 2 (p. 400) 1, 6, 7
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Note: Please label your homework assignment as shown above along with your name.
Grade Tracking
Homework Quiz #1
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Homework Quiz #2
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Homework Quiz #3
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Homework Quiz #4
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Problem Solving
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Unit 3 Test
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Unit 3 Points Earned
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Unit 3 Possible Points
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Unit 3 Average
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Unit 3 Grade
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Cumulative Average
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Cumulative Grade
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Algebra 2 Concepts - Unit 3 (textbook sections 5.1 – 5.9)
The end behavior of a function’s graph is the direction the function goes as x approaches positive
infinity (x→ +∞) or as x approaches negative infinity (x→ −∞). For polynomial functions, the end
behavior is determined by the function’s degree and the sign of its leading coefficient. When the
degree is odd (linear, cubic, quintic, etc.), you will see one end going up and one end going down.
Odd-degree functions with a positive leading coefficient will increase, and those with a negative
leading coefficient will decrease, as x approaches positive infinity. When the degree is even
(quadratic, quartic, etc.), you will either see both ends going up, or both ends going down. Evendegree functions with a positive leading coefficient will open upward, and those with a negative
leading coefficient will open downward.
The Fundamental Theorem of Algebra states that a polynomial of degree n has at least one
solution in the set of complex numbers, which includes all real and imaginary numbers.
Furthermore, if repeated solutions are counted separately, then a polynomial of degree n has exactly
n solutions. In other words, this means that an nth-degree polynomial will have exactly n zeros,
which can be either real or imaginary, with the real zeros being the x-intercepts of the graph.
The local extreme values of a function are places where its graph changes direction, either from
up to down, or from down to up. The y-coordinate of a turning point is a local maximum if the
point is higher than the other points around it, and it is a local minimum if the point is lower than
the other points around it. The graph of a polynomial of degree n has at most n − 1 local extreme
values, or turning points.
The finite differences of a polynomial function are the differences in the y-values given equally
spaced x-values. If these first-order differences are constant, then the polynomial is linear, or 1st
degree. If they are not constant, then a second set of differences can be calculated from them. If
these second-order differences are constant, then the polynomial is quadratic, or 2nd degree. If they
are not constant, then a third set can be calculated, and so on. Thus, the general rule for polynomial
functions is that an nth-degree polynomial will have constant nth-order differences.