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dolla averas Headow alks in Portfolio Entry Polynomial functions 1 a cit Investigate the leading co-efficient, "a" of a polynomial function from a table of values. ousa [3] Recall n!= n(n -1)(n -2)...3(2)(1), 1! =1 Calculate 2! = low b) In each of these linear models try to find a simple equation that connects the value of "a" to the , 3 ! = _ _ and 4! = 1 st difference, "Istdiff." Fill in the blanks i) [3] the charts' Istdiff columns ii) [2]a values, ds y = 2x+1;a=2 iii) [1 ] the third equation X Y y = 3x-1;a= 0 Istdiff X Y y = Istdiff X Y Istdiff 0 2 19 14 iv) [1] In a linear model what is the equation that relates a to the Istdiff, d? c) In each of these quadratic models try to find a simple equation that connects the value of "a" to the 1 st difference, "Istdiff." Fill in the blanks i) [3] the charts' missing values ii) [2]a values, iii) [1 ] the third y= x'+x+1;a=1 equation y = 2x2; a= y= ; a = X Y Istdiff 2nddiff X Y Istdiff 2nddiff X Y 0 1 stdiff 2nddiff 10 1 3 0 10 2 15 2 8 20 3 13 18 45 iv) [1]In a quadratic model what is the equation that relates a to the 2nddiff, d? d) In each of these quadratic models try to find a simple equation that connects the value of " a" to the 1st difference, "Istdiff." Fill in the blanks i) [3] the charts' ii) [2]a values, iii) [1] the second missing values equation y = 2x' +1; a= y = a= X Y Istdiff 2nddiff 3rddiff X Y Istdiff 2nddiff 3rddiff 0 0 1 3 1 3 17 24 2 2 81 3 55 3 4 192 4 129 iv) [1]In a cubic model what is the equation that relates a to the 3raddiff, d? e) [1] What is the general formula relating the no difference, (nthdiff, "d") in a table of an n' degree polynomial function to the equation's leading co-efficient "a"? Consider the n! values from part a, and your conclusions in parts iv) of b, c and d; your answer here should no be very complicated