Personalized Polynomial Creating the polynomial that passes through a set of letter-points from a word. x-cordinate of a letter-point is the position of the letter in the word. The first letter has a position of one, the second letter has a position of two... The y-cordinate of the letter-point is the depth of the letter in the alphabet. A has a depth of 1, B has a depth of two... The word for this personalized polynomial is “SAMUEL”. ClearAll; Defining the Polynomial The word “SAMUEL” is six letters long. Part S Defining the part of the polynomial for “S”. “S” is the first letter in “SAMUEL” and the 19th letter of the alphabet. [email protected]_D:=19*[email protected], 8i, 2, 6<D [email protected], 8i, 2, 6<D; Part A Defining the part of the polynomial for “A”. “A” is the second letter in “SAMUEL” and the 1st letter of the alphabet. [email protected]_D:=1*[email protected], 8i, 1, 1<D*[email protected], 8i, 3, 6<D [email protected], 8i, 1, 1<D*[email protected], 8i, 3, 6<DL; Part M Defining the part of the polynomial for “M”. “M” is the third letter in “SAMUEL” and the 13th letter of the alphabet. [email protected]_D:=13*[email protected], 8i, 1, 2<D*[email protected], 8i, 4, 6<D [email protected], 8i, 1, 2<D*[email protected], 8i, 4, 6<DL; Part U Defining the part of the polynomial for “U”. “U” is the forth letter in “SAMUEL” and the 21st letter of the alphabet. 4/5/14 B Group [email protected]_D:=21*[email protected], 8i, 1, 3<D*[email protected], 8i, 5, 6<D [email protected], 8i, 1, 3<D*[email protected], 8i, 5, 6<DL; Part E Defining the part of the polynomial for “E”. “E” is the fifth letter in “SAMUEL” and the fifth letter of the alphabet. [email protected]_D:=5*[email protected], 8i, 1, 4<D*[email protected], 8i, 6, 6<D [email protected], 8i, 1, 4<D*[email protected], 8i, 6, 6<DL; Part L Defining the part of the polynomial for “L”. “L” is the sixth letter in “SAMUEL” and the twelveth letter of the alphabet. [email protected]_D:=12*[email protected], 8i, 1, 5<D [email protected], 8i, 1, 5<D; Tying It Together Defining the polynomial as the sum of all of its parts. In[938]:= [email protected]_D:= [email protected] + [email protected] [email protected] [email protected] + [email protected] + [email protected]; [email protected]@xDD 1 Out[939]= 120 I7440 - 4018 x - 3595 x2 + 3125 x3 - 725 x4 + 53 x5 M Displaying the Polynomial Displaying the Polynomial in a Chart In[940]:= [email protected], 8i, 6<D; [email protected]@iD, 8i,6<D; TableData= [email protected], Outputs1<D; [email protected], TableHeadings® 8None, 8"Input", "Output"<<D Out[943]//TableForm= Input 1 2 3 4 5 6 Output 19 1 13 21 5 12 Page 2 of 4 Weaver Personalized Polynomial.nb | Displaying the Polynomial in a Graph The Points and Their Labels [email protected]@8Orange, [email protected],19<, 8.04,1<D<D, [email protected]@[email protected]"S", Large, Bold, BlueD, 81.07, 21.5<DDD; [email protected]@8Orange, [email protected],1<, 8.04,1<D<D, [email protected]@[email protected]"A", Large, Bold, BlueD, 82, 4<DDD; [email protected]@8Orange, [email protected],13<, 8.04,1<D<D, [email protected]@[email protected]"M", Large, Bold, BlueD, 82.9, 15.8<DDD; [email protected]@8Orange, [email protected],21<, 8.04,1<D<D, [email protected]@[email protected]"U", Large, Bold, BlueD, 84.05, 23.5<DDD; [email protected]@8Orange, [email protected],5<, 8.04,1<D<D, [email protected]@[email protected]"E", Large, Bold, BlueD, 85.07, 8<DDD; [email protected]@8Orange, [email protected],12<, 8.04,1<D<D, [email protected]@[email protected]"L", Large, Bold, BlueD, 85.95, 14.8<DDD; [email protected], A2, M2, U2, E2, L2D; The Domain and Range In[951]:= MinDomain=0; MaxDomain=7; [email protected]@i1000D, 8i, 1000*MinDomain, 1000*MaxDomain<D; [email protected]@Outputs2DD; [email protected]@Outputs2DD; [email protected]; The Function In[961]:= [email protected]@xD, 8x, MinDomain, MaxDomain<, AxesLabel® 8"Input", "Output"<, PlotStyle®Blue, PlotRange® 8MinRange-10100*Range1, MaxRange-60100*Range1<, PlotLabel® "Personalized Polynomial"D; 3 4/5/14 B Group Weaver Tying It Together In[962]:= [email protected], DataPointsAndLabelsD Personalized Polynomial Output 80 60 40 Out[962]= 20 U S M L E A 1 2 Input 3 4 -20 Page 4 of 4 5 6 7

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