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									MHF 4U0

             3.3 Characteristics of Polynomial Functions in Factored Form
For each set of polynomial functions:
   (a) Sketch the function using the graphing calculator
   (b) Note of the zeroes, and the shape of the graph as it passes through each zero
   (c) Note the approximate maximum or minimum points (ie. turning points) using the TRACE
       function
SET A
(i)      y = x(x + 2)(x – 2)           (ii)     y = x2(x + 2)(x – 2)             (iii)    y = x3(x + 2)(x – 2)




SET B
(i)      y = –x(x + 3)(x – 3)          (ii)     y = –x2(x + 3)(x – 3)            (iii)    y = –x3(x + 3)(x – 3)




SET C
(i)      y = x(x + 2)(x – 2)           (ii)     y = x(x + 2)2(x – 2)             (iii)    y = x(x + 2)3(x – 2)




SET D
(i) y = (x + 1)(x – 1)(x + 2)(x – 2)   (ii) y = (x + 1)(x – 1)2(x + 2)2(x – 2)   (iii) y = (x + 1)(x – 1)3(x + 2)2(x – 2)
MHF 4U0

                 3.3 Characteristics of Polynomial Functions in Factored Form

Family of Polynomial Functions:
      A set of polynomial functions whose equations have the same degree and whose graphs
       have the same characteristics (ie. shape, zeroes (see pg139 at bottom), vertex)

Example #1:
   (a) Determine the family of functions of degree 3 with zeroes 5, –3, and 2.
   (b) Determine the specific family member which passes through the point (–1, 24).




Example #2:
   (a) Find the roots (x-intercepts) of the function f(x) = 3x3 – 4x2.




   (b) Sketch the graph of the function on the grid provided.




Assigned Work: page 146 #1(pair share), 2b, 3, 4b, 5, 6bcd, 8b, 9ac, 10b, 13b

								
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