II. Bottle Design For Ladies'Perfume and Men's Cologne This project is based on Families of Polynomial Functions. The use of Technology is recommended when creating the bottle designs for the Chapter Problem Wrap-Up. Use free graphing software such as Winplot and Desmos. You may use animation and colour can results in some very attractive design. The following tips may benefit all students especially those having difficulty getting started with their designs Choose a degree of your polynomial function Select the x-intercepts Graph the functions Reflect it in the x-axis Change the leading coefficient to create a family of functions Apply the knowledge of transformations to create interesting designs. Level 3 Sample Response Bortle Design for Ladies Perfume 5 1 0.5 O OSS a The family of functions that was used is y = a(x - 3)(x - 2)(2x + 3)(2x - 1)2 Top part: y = a(x - 3)(x - 2)(2x + 3) (2x - 1)2 +1 where a = 0.01, 0.02.0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09 Bottom part: y = a(x - 3)(x - 2)(2x + 3)(2x - 1)2 - 1 where a = -0.01,-0.02. - 0.03, -0.04 -0.05. - 0.06,-0.07- 0.08- 0.09. Domain: * E R.[x = -1.7.2.9] X-intercepts: -1.5, 0.5(order 2), 2, and 3 Design with Bottle Design for Men Cologne Then 1.5 10.50 0.5 1 1.5 2 The family functions that was used to create this design is y = a(2x + 3)(x-2)(2x + 1)2 Top part: y = a(2x + 3)(x-2)(2x + 1)2 + 2 where a = -0.200,- 0.175,-0.150,- 0.100, - 0.075, -0.050,- 0.0250 Bottom part: y = a(2x + 3)(x - 2)(2x + 1)2 - 2 where a =0.200, 0.175, 0.150, 0.100, 0.075, 0.050, 0.0250 Domain: * E R. [x -1.8, 2.2] X-intercepts: -1.5, -0.5(order 2), and 2 Rubric for Task 1: Part A-II Bottle Design Category Level 4 Level 3 Level 2 Level 1 (8-10) (7-7.9) (6-6.9) (5.9 below) Knowledge and Has high degree Has considerable Has some of Has limited Understanding of understanding degree of understanding to degree of (10marks) to determine the understanding to determine the understanding to real roots of the determine the real real roots of the determine the equations and roots of the equations and real roots of the their connection equations and their connection equations and to the x- their connection to the x- their connection intercepts of the to the x-intercepts intercepts of the to the X- corresponding of the corresponding intercepts of the graphs. corresponding graphs. corresponding graphs. graphs. Thinking and Excellent Good Some No or little Inquiry understanding of understanding of understanding of understanding of (10marks) techniques to techniques to techniques to techniques to solve equations solve equations solve equations solve equations and inequalities. and inequalities. and inequalities and inequalities. Clear with high Some Little No justification justification or justification or justification or or reasoning for reasoning for reasoning for reasoning for choices made. choices made. choices made. choices made. Communication Very interesting, Interesting and Simple and not No design (10marks) creative, and somewhat very complex created for the complex design complex design design created task created with a created with a with a few variety of curves. numerous curves. curves. Application (10marks) Thorough Fairly organized Somewhat Not organized organized and and logical organized and and no logical logical solutions. solutions, logical solutions. solutions. Solutions to all Solutions to most Solutions to No solutions parts required are parts required are some parts provided. provided, and are provided, and required are all accurate may contain very provided, and minor errors. solutions may contain some errors. II. Bottle Design For Ladies'Perfume and Men's Cologne This project is based on Families of Polynomial Functions. The use of Technology is recommended when creating the bottle designs for the Chapter Problem Wrap-Up. Use free graphing software such as Winplot and Desmos. You may use animation and colour can results in some very attractive design. The following tips may benefit all students especially those having difficulty getting started with their designs Choose a degree of your polynomial function Select the x-intercepts Graph the functions Reflect it in the x-axis Change the leading coefficient to create a family of functions Apply the knowledge of transformations to create interesting designs. Level 3 Sample Response Bortle Design for Ladies Perfume 5 1 0.5 O OSS a The family of functions that was used is y = a(x - 3)(x - 2)(2x + 3)(2x - 1)2 Top part: y = a(x - 3)(x - 2)(2x + 3) (2x - 1)2 +1 where a = 0.01, 0.02.0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09 Bottom part: y = a(x - 3)(x - 2)(2x + 3)(2x - 1)2 - 1 where a = -0.01,-0.02. - 0.03, -0.04 -0.05. - 0.06,-0.07- 0.08- 0.09. Domain: * E R.[x = -1.7.2.9] X-intercepts: -1.5, 0.5(order 2), 2, and 3 Design with Bottle Design for Men Cologne Then 1.5 10.50 0.5 1 1.5 2 The family functions that was used to create this design is y = a(2x + 3)(x-2)(2x + 1)2 Top part: y = a(2x + 3)(x-2)(2x + 1)2 + 2 where a = -0.200,- 0.175,-0.150,- 0.100, - 0.075, -0.050,- 0.0250 Bottom part: y = a(2x + 3)(x - 2)(2x + 1)2 - 2 where a =0.200, 0.175, 0.150, 0.100, 0.075, 0.050, 0.0250 Domain: * E R. [x -1.8, 2.2] X-intercepts: -1.5, -0.5(order 2), and 2 Rubric for Task 1: Part A-II Bottle Design Category Level 4 Level 3 Level 2 Level 1 (8-10) (7-7.9) (6-6.9) (5.9 below) Knowledge and Has high degree Has considerable Has some of Has limited Understanding of understanding degree of understanding to degree of (10marks) to determine the understanding to determine the understanding to real roots of the determine the real real roots of the determine the equations and roots of the equations and real roots of the their connection equations and their connection equations and to the x- their connection to the x- their connection intercepts of the to the x-intercepts intercepts of the to the X- corresponding of the corresponding intercepts of the graphs. corresponding graphs. corresponding graphs. graphs. Thinking and Excellent Good Some No or little Inquiry understanding of understanding of understanding of understanding of (10marks) techniques to techniques to techniques to techniques to solve equations solve equations solve equations solve equations and inequalities. and inequalities. and inequalities and inequalities. Clear with high Some Little No justification justification or justification or justification or or reasoning for reasoning for reasoning for reasoning for choices made. choices made. choices made. choices made. Communication Very interesting, Interesting and Simple and not No design (10marks) creative, and somewhat very complex created for the complex design complex design design created task created with a created with a with a few variety of curves. numerous curves. curves. Application (10marks) Thorough Fairly organized Somewhat Not organized organized and and logical organized and and no logical logical solutions. solutions, logical solutions. solutions. Solutions to all Solutions to most Solutions to No solutions parts required are parts required are some parts provided. provided, and are provided, and required are all accurate may contain very provided, and minor errors. solutions may contain some errors