IM 3 Assignment 4.3 : Graph Investigation Unit 4 Polynomial Functions
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- Sherilyn Shana Flowers
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1 (A) Lesson Context BIG PICTURE of this UNIT: What is a Polynomial and how do they look? What are the attributes of a Polynomial? How do I work with Polynomials? CONTEXT of this LESSON: Where we ve been We have discussed the basics: degree, type, and operations (+,, x) Where we are What are the key attributes of a polynomial and how do these affect the shape? Where we are heading What are the key attributes of a polynomial and how do these affect the shape? (B) Lesson Objectives: a. Work on and attempt to develp an understanding of KEY Vocabulary. b. Begin to analyze the the attributes of a polynomial function and it s effect on the graph. c. Observations and patterns in the graphs of polynomials. d. Solidify our perdictions of how polynomials behave. (C) Some Context Lets try and get a grasp on what a Polynomail is, and then we will attempt to develop an understanding of the related vocabulary. So first, some context. In each of the senarios below please come up with an appropriate polynomial that models each situation. Part 1: Graph Exploration: You will be using Desmos to develop sketches of our given polynomials functiosn. You will then be asked to make some observations about attributes of the polunomials functions and how those attributes affect the graphs.
2 1. For the two equations below, please complete the tables for each in a different color. y = 2x + 5 y = x x + y = 5 -x +2y = -5 Degree of Polynomial: 1 2, -1 Constant Term: 5, -5/2 Positive or Negative 2, -1 X Intercepts: 5/2, 5 Y Intercept: 5, -5/2 Y Min: -10 Y Max: 10
3 2. For the two equations below, please complete the tables for each in a different color. y = (3x 1)(x + 2) y = (4 x)(x + 3) y = 3x 2 + 5x 2 y = -x 2 + x + 12 Degree of Polynomial: 2 3, -1 Constant Term: -2, 12 Positive or Negative 3, -1 X Intercepts: 1/3, 2 & 4, -3 Y Intercept: -2 & 12 X Min: -5 X Max: 5 Y Min: -5 Y Max: 15
4 3. For the two equations below, please complete the tables for each in a different color. y = (x 4)(x + 5) y = (5 x)(x + 4) y = x 2 + x 20 y = -x 2 + x + 20 Degree of Polynomial: 2 1, -1 Constant Term: -20, 20 Positive or Negative 1, -1 X Intercepts: 4, -5 & 5, -4 Y Intercept: -20 & 20 Y Min: -25 Y Max: 25
5 4. For the two equations below, please complete the tables for each in a different color. y = -(x 3)(x 1)(x +1) y = (x + 4)(x 1)(x 5) y = -x 3 + 3x 2 + x 3 y = x 3 2x 2 19x + 20 Degree of Polynomial: 3-1, 1 Constant Term: -3, 20 Positive or Negative 1, -1 X Intercepts: -3, 1, -1 & -4, 1, 5 Y Intercept: -3, 20 Y Min: -50 Y Max: 50
6 5. For the two equations below, please complete the tables for each in a different color. y = (x 1)(x + 2)(x +6) y = -x(x 3)(x + 3) y = x 3 + 7x 2 + 4x 12 y = -x 3 + 9x Degree of Polynomial: 3 1, -1 Constant Term: -12, 0 Positive or Negative 1, -1 X Intercepts: -6, -2, 1 & -3, 0, 3 Y Intercept: -12, 0 Y Min: -15 Y Max: 25
7 6. For the two equations below, please complete the tables for each in a different color. y = -x(x 1.5)(x + 1.5)(x 2) y = (x 3)(x 1)(x + 1)(x +3) Cubic, Quartic, Quintic y = -x 4 +2x x 2 4.5x y = x 4 10x Degree of Polynomial: 4-1, 1 Constant Term: 0, 9 Positive or Negative 1, -1 X Intercepts: -1.5, 0, 1.5, 2 & -3, -1, 1, 3 Y Intercept: 0, 9 X Min: -4 X Max: 4 Y Min: -20 Y Max: 20
8 7. For the two equations below, please complete the tables for each in a different color. y = x (x 2)(x + 2)(x + 4) y = (x +1)(x 3)(x 6)(x 1) y = x 4 20x y = 2x 4 39x x 2 621x Trinomial, Polynomial Degree of Polynomial: 4 1, 2 Constant Term: 64, 486 Positive or Negative 1, 2 X Intercepts: -4, -2, 2, 4 & 2/3, 3, 6, 9 Y Intercept: 64, 486 Y Min: -150 Y Max: 150
9 8. For the two equations below, please complete the tables for each in a different color. y = (x 4)(x 2)(x + 7)(x 5)(x + 2) y = x(x + 1)(x + 3)(x 1)(x + 4) Cubic, Quartic, Quintic y = x 5 2x 4 47x x x 560 y = x 5 + 7x x 3 7x 2 12x Trinomial, Polynomial Degree of Polynomial: 5 1 Constant Term: -560, 0 Positive or Negative 1 X Intercepts: -7, -2, 2, 4, 5 & -4, -3, -1, 0, 1 Y Intercept: -560, 0 Y Min: Y Max: 4500
10 9. For the two equations below, please complete the tables for each in a different color. y = (x 1)(x 2)(x 3)(x 4)(x 5) y = (x 5)(x + 1)(x + 3)(x + 4)(x 1) Cubic, Quartic, Quintic y = x 5 15x x 3 225x x 120 y = x 5 + 2x 4 24x 3 62x x + 60 Trinomial, Polynomial Degree of Polynomial: 5 1 Constant Term: -120, 60 1 Positive or Negative X Intercepts: 1, 2, 3, 4, 5 & -4, -3, -1, 1, 5 Y Intercept: -120, 60 Y Min: -150 Y Max: 100
11 Connections: What connections do you see between the x intercepts and either of the equations? What connections do you see between the y intercepts and the equations? What connections do you see between the SHAPE of the graph and the DEGREE?? What connections do you see betweenthe SHAPE of the graph and the Leading Coefficient?
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