Graphing Utility Programs

Transcription

1 Appendix H Graphing Utility Programs H1 Appendix H Graphing Utility Programs Parabola (Reflections and Shifts Program) Reflections and Shifts Program (Section 2.6) This program will graph the function y R x H 2 V, where R ±1, H is an integer between 6 and 6, and V is an integer between 3 and 3. This program gives you practice working with reflections, horizontal shifts, and vertical shifts. TI-80 PROGRAM:PARABOL :-6+INT (12RAND) H :-3+INT (6RAND) V :RAND R :IF R <.5 :THEN :-1 R :ELSE :1 R :END : R(X+H) 2+V Y1 :-9 XMIN :9 XMAX :1 XSCL :-6 YMIN :6 YMAX :1 YSCL :DISPGRAPH :PAUSE :DISP Y=R(X+H) 2+V 2 :DISP R=,R :DISP H=,H :DISP V=,V :PAUSE Press ENTER after viewing the graph to display the values TI-81 Prgm4:PARABOLA :Rand H :-6+Int (12H) H :Rand V :-3+Int (6V) V :Rand R :If R <.5 :-1 R :If R >.49 :1 R : R(X+H) 2+V Y1 :-9 Xmin :9 Xmax :1 Xscl :-6 Ymin :6 Ymax :1 Yscl :DispGraph :Disp Y=R(X+H) 2+V :Disp R= :Disp R :Disp H= :Disp H :Disp V= :Disp V Press ENTER after viewing the graph to display the values TI-82 TI-83 TI-83 Plus PROGRAM:PARABOLA :-6+int (12rand) H :-3+int (6rand) V :rand R :If R <.5 :Then :-1 R :Else :1 R : R(X+H) 2+V Y1 :-9 Xmin :9 Xmax :1 Xscl :-6 Ymin :6 Ymax :1 Yscl :DispGraph :Disp Y=R(X+H) 2+V :Disp R=,R :Disp H=,H

2 H2 Appendix H Graphing Utility Programs :Disp V=,V Press ENTER after viewing the graph to display the values TI-85 TI-86 :rand H :-6+int (12H) H :rand V :-3+int (6V) V :rand R :If R <.5 :-1 R :If R >.49 :1 R :y1=r(x+h) 2+V :-9 xmin :9 xmax :1 xscl :-6 ymin :6 ymax :1 yscl :DispG :Disp Y=R(X+H) 2+V :Disp R=,R :Disp H=,H :Disp V=,V Press ENTER after viewing the graph to display the values TI-92 :parabola( ) :Prgm :ClrIO :setmode( Split Screen, Left-Right ) :setmode( Split 1 App, Home ) :setmode( Split 2 App, Graph ) :-6+int (12rand( )) h :-3+int (6rand( )) v :rand( ) r :If r <.5 Then : -1 r : Else : 1 r If :r*(x+h)^2+v y1(x) :-9 xmin :9 xmax :1 xscl :-6 ymin :6 ymax :1 yscl :DispG :Disp y1(x)=r(x+h)^2+v :Output 20,1, r= :Output 20,11,r :Output 40,1, h= :Output 40,11,h :Output 60,1, v= :Output 60,11,v :setmode( Split Screen, Full ) Prgm Casio fx-7700g PARABOLA -6+INT (12Ran#) H -3+INT (6Ran#) V -1 R:Ran#<0.5 1 R Range -9,9,1,-6,6,1 Graph Y=R(X+H)2+V Y=R(X+H)2+V R= :R H= :H V= :V Press EXE after viewing the graph to display the values Casio fx-7700ge Casio fx-9700ge Casio CFX-9800G PARABOLA -6+Int (12Ran#) H -3+Int (6Ran#) V Ran# R R<.5-1 R R.5 1 R Range -9,9,1,-6,6,1 Graph Y=R(X+H)2+V Y=R(X+H)2+V R= :R H= :H V= :V Press EXE after viewing the graph to display the values

3 Appendix H Graphing Utility Programs H3 Casio CFX-9850G Use the previous program and replace the line Range -9,9,1,-6,6,1 with View Window -9,9,1,-6,6,1,. Press EXE after viewing the graph to display the values Sharp EL-9200C Sharp EL-9300C parabola REAL h=int (random*12) -6 v=int (random*6) -3 s=(random*2) -1 r=s/abs s Range -9,9,1,-6,6,1 Graph r(x+h) 2+v Wait Print y=r(x+h) 2+v Print r Print h Print v End Press ENTER after viewing the graph to display the values 8. Press OK to return to the graph. 9. Repeat steps 6, 7, and 8 for a new parabola. PARABOLA PROGRAM -6+INT(12RANDOM) H: -3+INT(6RANDOM) V: RANDOM R: IF R>.5 THEN -1 R: ELSE 1 R: END: R*(X+H) 2+V F1(X): CHECK 1: PARANS PROGRAM ERASE: DISP 2; Y=R(X+H) 2+V : DISP 3; R= R: DISP 4; H= H: DISP 5; V= V: FREEZE: PARABOLA.SV PROGRAM SETVIEWS RUN PARABOLA ;PARABOLA;1; ANSWER ;PARANS;1; ;PARABOLA.SV;0: HP 38G This program will sketch a graph of the function y R x H 2 V, where R ±1, H is an integer between 6 and 6, and V is an integer between 3 and 3. This program gives you practice working with reflections, horizontal shifts, and vertical shifts. 1. Press LIB. Highlight the Function aplet. Press SAVE. Enter the name PARABOLA for the new aplet and press OK. 2. Press [SETUP-PLOT] and set XRNG: from 12 to 12, YRNG: from 6 to 6, and XTICK: and YTICK: to Enter the 3 programs PARABOLA, PARANS, PARABOLA.SV. 4. Run the program PARABOLA.SV. 5. Enter the PARABOLA aplet. 6. Press [VIEWS]. Highlight RUN PARABOLA and press OK. 7. After viewing the graph press [VIEWS]. Highlight ANSWER and press OK to see the values of the integers.

4 H4 Appendix H Graphing Utility Programs Two-Point Form of a Line (Section 3.1) This program, will display the slope and y-intercept of the line that passes through two points, x 1, y 1 and x 2, y 2, entered by the user. TI-80 PROGRAM:TWOPTFM :DISP ENTER X1, Y1 :INPUT X :INPUT Y :DISP ENTER X2, Y2 :INPUT C :INPUT D : D Y C X M : M -X Y B :DISP SLOPE = :DISP M :DISP Y-INT = :DISP B TI-81 TI-82 TI-83 TI-83 Plus PROGRAM:TWOPTFM :Disp ENTER X1, Y1 :Input X :Input Y :Disp ENTER X2, Y2 :Input C :Input D : D Y C X M :M* -X Y B :Disp SLOPE = :Disp M :Disp Y-INT = :Disp B TI-85 TI-86 PROGRAM:TWOPTFM :Disp Enter X1, Y1 :Input X :Input Y :Disp Enter X2, Y2 :Input C :Input D : D Y C X M :M* -X Y B :Disp Slope = :Disp M :Disp Y-int = :Disp B TI-92 :twoptfm ( ) :Prgm :Disp ENTER X1, Y1 :Input x :Input y :Disp ENTER X2, Y2 :Input c :Input d : d y c x m :m*-x y b :Disp SLOPE = :Disp m :Disp Y-INT = :Disp b Prgm Casio fx-7700g TWOPTFORM ENTER X1, Y1? X:? Y ENTER X2, Y2? C:? D D Y C X M M -X Y B SLOPE = :M Y-INT = :B Casio fx-7700ge Casio fx-9700ge Casio CFX-9800G TWOPTFORM ENTER X1, Y1? X:? Y ENTER X2, Y2? C:? D D Y C X M M -X Y B SLOPE = :M Y-INT = :B Casio CFX-9850G ======TWOPTFM====== ENTER X1, Y1? X:? Y ENTER X2, Y2? C:? D D Y C X M M -X Y B SLOPE = :M Y-INT = :B

5 Appendix H Graphing Utility Programs H5 SHARP EL-9200C SHARP EL-9300C twoptform Print enter x1, y1 Input x c=x Input y d=y Print enter x2, y2 Input x Input y m= d y c x b= m* -x y Print slope Print m Print y-int Print b HP 38G TWOPTFM PROGRAM INPUT X: ENTER X1, Y1 ; ENTER X1 ;;1: INPUT Y: ENTER X1, Y1 ; ENTER Y1 ;;1: INPUT C: ENTER X2, Y2 ; ENTER X2 ;;1: INPUT D: ENTER X2, Y2 ; ENTER Y2 ;;1: D Y C X M M*-X Y B DISP 1; SLOPE = M: DISP 3; Y-INT = B; FREEZE: Simple Interest Program (Section 3.3) This program can be used to find the amount of simple interest earned on a given principal at a given annual interest rate for a certain amount of time. TI-80 PROGRAM:SIMPINT :FIX 2 :DISP PRINCIPAL :INPUT P :DISP INTEREST RATE :DISP IN DECIMAL FORM :INPUT R :DISP NUMBER OF YEARS :INPUT T :PRT I :DISP THE INTEREST IS :DISP I :FLOAT TI-81 TI-82 TI-83 TI-83 Plus PROGRAM:SIMPINT :Fix 2 :Disp PRINCIPAL :Input P :Disp INTEREST RATE :Disp IN DECIMAL FORM :Input R :Disp NUMBER OF YEARS :Input T :PRT I :Disp THE INTEREST IS :Disp I :Float TI-85 TI-86 PROGRAM:SIMPINT :Fix 2 :Disp Principal :Input P :Disp Interest rate :Disp in decimal form :Input R :Disp Number of years :Input T : P*R*T I :Disp The interest is :Disp I :Float

6 H6 Appendix H Graphing Utility Programs TI-92 :simpint ( ) :Prgm :setmode( Display Digits, Fix 2 ) :Input Principal, p :Input Interest rate in decimal form, r :Input Number of years, t :p*r*t i :Disp The interest is, i :setmode( Display Digits, Float ) Prgm Casio fx-7700g SIMPINT Fix 2 PRINCIPAL? P INTEREST RATE IN DECIMAL FORM? R NUMBER OF YEARS? T PRT I THE INTEREST IS :I Norm Casio fx-7700ge Casio fx-9700ge Casio CFX-9800G Casio CFX-9850G SIMPINT Fix 2 PRINCIPAL? P INTEREST RATE IN DECIMAL FORM? R NUMBER OF YEARS? T PRT I THE INTEREST IS :I Norm Sharp EL-9200C Sharp EL-9300C simpint REAL Input principal Print Interest rate Print in decimal form Input rate Print Number of years Input time interest= principal*rate*time Print interest HP 38G SIMPINT PROGRAM INPUT P; SIMPINT ;; ENTER PRINCIPAL ;1: INPUT R; SIMPINT ;; INTEREST RATE IN DECIMAL FORM ;1: INPUT T; SIMPINT ;; ENTER NUMBER OF YEARS ;1: P*R*T I: DISP 3; INTEREST IS I: FREEZE:

7 Appendix H Graphing Utility Programs H7 Quadratic Formula Program (Section 6.3) This program will display the solutions to quadratic equations or the words No Real Solution. To use the program, write the quadratic equation in standard form and enter the values of a, b, and c. TI-80 PROGRAM:QUADRAT :Disp AX 2 BX C=0 :Input ENTER A,A :Input ENTER B, B :Input ENTER C, C :B 2 4AC D :If D 0 :Then : -B D 2A M :Disp M : -B D 2A N :Disp N :Else :Disp NO REAL SOLUTION TI-81 TI-82 TI-83 TI-83 Plus PROGRAM:QUADRAT :Disp AX 2 BX C=0 :Prompt A :Prompt B :Prompt C :B 2 4AC D :If D 0 :Then : -B D 2A M :Disp M : -B D 2A N :Disp N :Else :Disp NO REAL SOLUTION TI-92 :quadrat( ) :Prgm :setmode( Complex Format, RECTANGULAR ) :Disp AX 2 BX C=0 :Input Enter A.,a :Input Enter B.,b :Input Enter C.,c :b 2 4*a*c d : -b d 2*a m : -b d 2*a n :Disp m :Disp n :setmode( Complex Format, REAL ) Prgm This program gives both real and complex answers. Prgm4: QUADRAT :Disp ENTER A :Input A :Disp ENTER B :Input B :Disp ENTER C :Input C :B 2 4AC D :If D<0 :Goto 1 : -B D 2A M :Disp M : -B D 2A N :Disp N :Lbl 1 :Disp NO REAL :Disp SOLUTION TI-85 TI-86 PROGRAM:QUADRAT :Disp AX 2 BX C=0 :Input ENTER A,A :Input ENTER B, B :Input ENTER C, C :B 2 4*A*C D : -B D 2A M :Disp M : -B D 2A N :Disp N This program gives both real and complex answers. Solutions to quadratic equations are also available directly by using the POLY function. Casio fx-7700g QUADRATIC AX 2 BX C=0 A=? A B=? B C=? C B 2 4AC D D<0 Goto 1 X= : -B D 2A OR X= : -B D 2A Goto 2 Lbl 1 NO REAL SOLUTION Lbl 2

8 H8 Appendix H Graphing Utility Programs Casio fx-7700ge QUADRATIC AX 2 BX C=0 A=? A B=? B C=? C B 2 4AC D D<0 Goto 1 -B D 2A -B D 2A Goto 2 Lbl 1 NO REAL SOLUTION Lbl 2 Solutions to quadratic equations are also available directly from the Casio calculator s EQUATION MODE. Casio fx-9700ge Casio CFX-9800G QUADRATIC AX 2 BX C=0 A=? A B=? B C=? C B 2 4AC D -B D 2A -B D 2A Both real and complex answers are given. Solutions to quadratic equations are also available directly from the Casio calculator s EQUATION MODE. Casio CFX-9850G ======QUADRAT====== AX 2 BX C=0 A=? A B=? B C=? C B 2 4AC D -B D 2A -B D 2A Both real and complex answers are given. Solutions to quadratic equations are also available directly from the Casio calculator s EQUATION MODE. Sharp EL-9200C Sharp EL-9300C quadratic COMPLEX Print ax 2 bx c=0 Input a Input b Input c d= b 2 4a*c x1= -b d 2a x2= -b d 2a Print x1 Print x2 End This program gives both real and complex answers. HP 38G QUADRAT PROGRAM INPUT A; AX 2 BX C=0 ; ENTER A ; ;1: INPUT B; AX 2 BX C=0 ; ENTER B ; ;1: INPUT C; AX 2 BX C=0 ; ENTER C ; ;1: B 2 4AC D: -B D 2A Z1: -B D 2A Z2: DISP 3;Z1: DISP 5;Z2: FREEZE This program displays the answer in complex form x, y, where x is the real part and y is the imaginary part.

9 Random Number Generator (Appendix D.1) This program will display ten randomly generated numbers. Repeatedly press ENTER or EXE until all ten integers are displayed. Appendix H Graphing Utility Programs H9 TI-80 PROGRAM:RANDOM :FOR(I, 1, 10) :INT(10RAND) A :DISP A :PAUSE :END TI-81 :Prgm2:RANDOM :1 I :Lbl 1 :Int(10Rand) A :Disp A :IS>(I,10) :Goto 1 :Disp DONE TI-82 TI-83 TI-83 Plus PROGRAM:RANDOM :For(I,1,10) :int(10rand) A :Disp A TI-85 TI-86 PROGRAM:RANDOM :For(I,1,10) :ipart(10rand) A :Disp A TI-92 :random ( ) :Prgm :For i,1,10 :ipart(10rand ( )) a :Disp a For :Disp DONE Prgm Casio fx-7700g RANDOM 0 C Lbl 1 C 1 C Int(10Ran#) A A C<10 Goto 1 Casio fx-7700ge Casio fx-9700ge Casio CFX-9800G RANDOM 1 I Lbl 1 Int 10Ran# Isz I I 10 Goto 1 DONE Casio CFX-9850G ======RANDOM====== 1 I Lbl 1 Int 10Ran# Isz I I 10 Goto 1 DONE Sharp EL-9200C Sharp EL-9300C random REAL i=0 Label 1 i=i+1 X=int 10random Print X Wait If i<10 Goto 1 End HP 38G RANDOM PROGRAM FOR I=1 TO 10 STEP 1; INT(10RANDOM) A: DISP 3;A: FREEZE: END

10 H10 Appendix H Graphing Utility Programs Birthday Problem Program (Appendix D.2) This program is a simulation of the birthday problem. The program displays the number of selections that were made before two people with the same birthday were found. Note to Casio users: The command Defm allocates additional memory for the storage of the random numbers generated in this program. The number 341 will allow the program to run and store 365 numbers without a memory error. You need to have 2728 bytes of memory available to run this program. If this amount of memory is not available in your graphing calculator, you may lower the number, but be aware you may receive a memory error when running the program. Consult your owner s manual for more information. TI-80 PROGRAM:BIRTHDA :CLRHOME :CLRLIST L1 : 0 C :DISP COMPUTING... :LBL A : 1 C C :IPART(365RAND) D : D L1 C :IF C=1:GOTO A :For(I,1,C 1) :If D=L1(I):GOTO B :END :GOTO A :LBL B :CLRHOME :DISP MATCH: NUMBER OF :DISP SELECTIONS IS :DISP C TI-81 Prgm 3:BIRTHDAY :ClrStat : 0 C :Disp COMPUTING... :Lbl A : 1 C C :IPart (365Rand) D : D x C :If C=1 :Goto A : 1 I :Lbl 1 :If D= x I :Goto B :IS>(I,C 1) :Goto 1 :Goto A :Lbl B :Disp MATCH, NUMBER OF :Disp SELECTIONS IS :Disp C TI-82 PROGRAM:BIRTHDAY :ClrList L1 : 0 C :Output(4,3, COMPUTING... ) :Lbl A : 1 C C :ipart (365rand) D :D L1(C) :If C=1:Goto A :For(I,1,C 1) :If D=L1(I):Goto B :Goto A :Lbl B :Disp MATCH: NUMBER OF :Disp SELECTIONS IS :Disp C

11 Appendix H Graphing Utility Programs H11 TI-83 TI-83 Plus PROGRAM:BIRTHDAY :ClrList L1 : 0 C :Output(4,3, COMPUTING... ) :Lbl A : 1 C C :randint(1,365) D :D L1(C) :If C=1:Goto A :For(I,1,C 1) :If D=L1(I):Goto B :Goto A :Lbl B :Disp MATCH: NUMBER OF :Disp SELECTIONS IS :Disp C TI-85 TI-86 PROGRAM:BIRTHDAY :C1LCD : 0 C :Outpt(4,3, COMPUTING... ) :Lbl A : 1 C C :ipart (365rand) D :D TEMP(C) :If C==1:Goto A :For(I,1,C 1) :If D==TEMP(I):Goto B :Goto A :Lbl B :ClLCD :Disp MATCH: NUMBER OF :Disp SELECTIONS IS :Disp C TI-92 :birthday ( ) :Prgm :ClrIO : 0 c :Output 4,3, COMPUTING... :Lbl a : 1 c c :ipart(365rand ( )) d :d list1[c] :If c=1:goto a :For i,1,c 1 :If d=list1[i]:goto b For :Goto a :Lbl b :ClrIO :Disp MATCH: NUMBER OF SELECTIONS IS :Disp c Prgm Casio fx-7700g BIRTHDAY Defm C COMPUTING... Lbl 1 1 C C Int (365Ran#) D D L[C] C=1 Goto 1 C 1 E Lbl 3 L[E]=D Goto 2 E 1 E E 0 Goto 3 Goto 1 Lbl 2 Defm 0 MATCH: NUMBER OF SELECTIONS IS :C Casio fx-7700ge Casio fx-9700ge Casio CFX-9800G BIRTHDAY Defm A COMPUTING... Lbl 1 Isz A Int (365ran#) B B D[A] A=1 Goto 1 1 C Lbl 2 B=D[C] Goto 3 Isz C C<A Goto 2 Goto 1 Lbl 3 Defm 0 MATCH: NUMBER OF SELECTIONS IS A

12 H12 Appendix H Graphing Utility Programs Casio CFX-9850G ======BIRTHDAY====== ClrText ClrList Seq(-1,A,1,250,1) List 1 Seq(-1,A,1,115,1) List 2 0 C Locate 4,3, COMPUTING... Lbl 1 Isz C Int (365Ran#) D If C 250 Then D List 1[C] Else D List 2[C 250] IfEnd If C=1 Then Goto 1 IfEnd For 1 I To C 1 Step 1 If I 250 Then List 1[I] E Else List 2[I 250] E IfEnd If D=E Then Goto2 IfEnd Next Goto1 Lbl 2 ClrText MATCH: NUMBER OF SELECTIONS IS C Sharp EL-9200C Sharp EL-9300C birthday STAT ClrT Stat X c=0 Print computing... Label a c=c+1 X=int 365random Data X If c=1 Goto a i=1 Label 1 If X=St[1,i] Goto b i=i+1 If i<c Goto 1 Goto a Label b ClrT Print match, number of Print selections is Print c HP 38G BIRTHDAY PROGRAM DISP 1; COMPUTING... : MAKELIST( 1,A,1,365,1) L1: 0 C: RUN GET NUMBER : DO RUN DO LOOP UNTIL D==E END: RUN PRINT ANSWER : FREEZE GET NUMBER PROGRAM 1 C C: INT(365RANDOM) D: D L1(C) DO LOOP PROGRAM RUN GET NUMBER : FOR I=1 TO C 1 STEP 1; IF D==L1(I) THEN L1(I) E END END PRINT ANSWER PROGRAM DISP 1; MATCH: NUMBER OF : DISP 2; SELECTIONS IS : DISP 3;C Enter the four programs (Birthday, Get Number, Do Loop, and Print Answer) into the HP 38G. Then RUN the Birthday program.