Grade 12 Advanced Functions MHF 4 U Unit

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Grade 12 Advanced Functions (MHF 4 U) Unit 1: Polynomial Functions Family of Polynomial

Grade 12 Advanced Functions (MHF 4 U) Unit 1: Polynomial Functions Family of Polynomial Functions Mr. Choi © 2017 E. Choi – MHF 4 U - All Rights Reserved

Family Functions A family of functions is a set of functions that have the

Family Functions A family of functions is a set of functions that have the same characteristics. Polynomial functions with the same zeros are said to belong to the same family. The graphs of polynomial functions that belong to the same family have the same x interceptbut have different y intercepts (Unless zero is one of the x intercept). An equation for the family of polynomial functions with zeros is where. Family of Polynomial Functions © 2017 E. Choi – MHF 4 U - All Rights Reserved

Example 1: Family Functions The zero of a family of quadratic functions are 2

Example 1: Family Functions The zero of a family of quadratic functions are 2 and -3. a) Determine an equation for this family functions. b) Write equations for two functions that belong to this family. c) Determine an equation for the member of the family that passes through the point (1, 4). Family of Polynomial Functions © 2017 E. Choi – MHF 4 U - All Rights Reserved

Example 2: Family Functions The zero of a family of cubic functions are -2,

Example 2: Family Functions The zero of a family of cubic functions are -2, 1 and 3. a) Determine an equation for this family functions. b) Write equations for two functions that belong to this family. c) Determine an equation for the member of the family whose graph has a y intercept of -15. d) Sketch graph of the function in part c). a) If roots are -2, 1 and 3, factors are (x + 2) , (x – 1) and (x – 3) respectively. An equation for this family is where b) For k = 2, For k = -1, c) Sub x = 0 and y = -15 into equation to solve for k. Y-intercept for c) is -15 Family of Polynomial Functions © 2017 E. Choi – MHF 4 U - All Rights Reserved

Example 3: Family Functions a) Determine a simplified equation for the family of quartic

Example 3: Family Functions a) Determine a simplified equation for the family of quartic functions with zeros and. b) Determine an equation for the member of the family whose graph passes through the point (2, 18). a) If roots are 1, -1 and , factors are (x – 1), (x + 1) , and respectively. b) Sub x = 2 and y = 18 into equation to solve for k. Family of Polynomial Functions © 2017 E. Choi – MHF 4 U - All Rights Reserved

Example 4: Family Functions Determine an equation for the quartic function in factors form

Example 4: Family Functions Determine an equation for the quartic function in factors form represented by this graph. From graph, the x intercepts are -3, -1/2, 1 and 2. The corresponding factors are (x + 3), (2 x + 1), (x – 1) and (x – 2) respectively. Select the point (-1, -6) and sub into the relation (-1, -6) Family of Polynomial Functions © 2017 E. Choi – MHF 4 U - All Rights Reserved

Homework Text Book • P. 119 # 1 – 3, 6, 7, 9, 11,

Homework Text Book • P. 119 # 1 – 3, 6, 7, 9, 11, 13, 15, 19 , 22 Check the website for updates Family of Polynomial Functions © 2017 E. Choi – MHF 4 U - All Rights Reserved

End of lesson Family of Polynomial Functions © 2017 E. Choi – MHF 4

End of lesson Family of Polynomial Functions © 2017 E. Choi – MHF 4 U - All Rights Reserved