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{SECT 0 {PARA 256 "" 0 "" {TEXT 264 47 "Precalculus Exploration 1: Qua
dratic Functions " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 265 87 "Use the following to explore and describe all possible e
ssentially different locations " }}{PARA 0 "" 0 "" {TEXT 266 82 "of th
e graph of a quadratic function and how this location depends on a, b,
 and c." }{TEXT -1 0 "" }{TEXT 267 0 "" }}{SECT 1 {PARA 3 "" 0 "" 
{TEXT -1 43 "Exploration Using Quadratic Function Solver" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT 256 37 "Enter your a , b, c values below for " }
{XPPEDIT 18 0 "f(x) = a*x^2+b*x+c;" "6#/-%\"fG6#%\"xG,(*&%\"aG\"\"\"*$
F'\"\"#F+F+*&%\"bGF+F'F+F+%\"cGF+" }{TEXT 268 12 " , and then " }}
{PARA 0 "" 0 "" {TEXT 259 46 "click in the red area below and press [E
nter]." }{MPLTEXT 1 0 61 "\nDigits:=5:\na:=2:#ENTER (a nonzero)\nb:=5:
#ENTER\nc:=-7:#ENTER\n" }{TEXT 257 59 "Define the function and then pr
int it and its end behavior." }{TEXT -1 1 "\n" }{MPLTEXT 1 0 237 "f:= \+
x -> a*x^2+b*x+c:\nif a < 0 then \n e_b:=`Down_Down`:\nelif a > 0 then
 \n e_b:=`Up_Up`:\nfi:\n`Coefficents:  `*'a'=a,'b'=b,'c'=c;\n`Standard
 form:  `*'f(x)'=f(x),\n`End Behavior: `*e_b;\n`Vertex form:  `*'f(x)'
=student[completesquare](f(x));\n" }{TEXT -1 0 "" }{TEXT 260 50 "Find \+
the vertex of the parabola and then print it." }{TEXT -1 0 "" }
{MPLTEXT 1 0 156 "\nx_vertex:=-b/(2*a):\ny_vertex:=-b^2/(4*a)+c:\nvert
ex:=[x_vertex,y_vertex]:\n'x_vertex'=x_vertex,`  `*'y_vertex'=y_vertex
;\n'vertex'=vertex*` = `*evalf(vertex);" }{TEXT -1 0 "" }{MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT 258 107 "Find any x-intercepts, the y-intercept, and then
 print them.\nClick in the red area below and press [Enter]." }{TEXT 
-1 0 "" }{MPLTEXT 1 0 275 "\nfactor(f(x))=0;\nsolns1:=sort([solve(f(x)
=0,x)]):\nsolns2:=sort(evalf(solns1)):\nx_inter1:=op(1,solns2):\nx_int
er2:=op(2,solns2):\nif Im(op(1,solns1)) = 0 then\n`x-intercept1`=x_int
er1,\n `  x-intercept2`=x_inter2;\nelse\n print(`No x-intercepts.`);\n
fi;\n`y-intercept = `*'f(0)'=f(0);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 102 "Set endpoin
ts for graphing window and then graph f(x). \nClick in the red area be
low and press [Enter]." }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }{MPLTEXT 1 0 124 "if Im(op(1,solns1)) = 0 then\n x_left:=x_inter1-2
:\n x_right:=x_inter2+2:\nelse\n x_left:=x_vertex-5:\n x_right:=x_vert
ex+5:\nfi:\n" }{TEXT -1 0 "" }{TEXT 262 64 "Create plot of graph of f(
x), including all points found above.\n" }{TEXT -1 0 "" }{MPLTEXT 1 0 
838 "p1:=plot(f(x),x=x_left..x_right,color=blue,linestyle=1):\npointco
lor:=`navy`:\nlinecolor:=`red`:\np2:=plot([[x_vertex,y_vertex]],style=
point,symbol=circle,color=pointcolor):\np3:=plot([[x_vertex,y_vertex],
[x_vertex,0]],linestyle=2,color=linecolor):\np4:=plot([[x_vertex,y_ver
tex],[0,y_vertex]],linestyle=2,color=linecolor):\np5:=plot([[0,f(0)]],
style=point,symbol=circle,color=pointcolor):\nif Im(op(1,solns1)) = 0 \+
then\n p6:=plot([[x_inter1,0]],style=point,symbol=circle,color=pointco
lor):\n p7:=plot([[x_inter2,0]],style=point,symbol=circle,color=pointc
olor):\nelse\n p6:=plot([[0,0]]):\n p7:=plot([[0,0]]):\nfi:\nParabolaP
lot:=\n plots[display](\n  [p1,p2,p3,p4,p5,p6,p7],\n  labels=[``,``],
\n  tickmarks=[5,9],\n  #view=[x_left..x_right,y_vertex-20..y_vertex+2
0],\n  titlefont=[HELVETICA,DEFAULT,14],\n  title=`Quadratic Function \+
Graph`):\n  ParabolaPlot;\n" }{TEXT -1 0 "" }{TEXT 263 30 "Display pre
vious information. " }{TEXT -1 0 "" }{MPLTEXT 1 0 226 "\n`Standard for
m:  `*'f(x)'=f(x),`End Behavior: `*e_b;\n'vertex'=evalf(vertex);\nif I
m(op(1,solns1)) = 0 then\n`x-intercept1`=x_inter1,\n `  x-intercept2`=
x_inter2;\nelse\n print(`No x-intercepts.`);\nfi;\n`y-intercept = `*'f
(0)'=f(0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 37 "_________________
____________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 30 "Filename: ExplorePrecalc01.mws" }}{PARA 0 "" 0 "" 
{TEXT -1 36 "Copyright 2005, All Rights Reserved." }}{PARA 0 "" 0 "" 
{TEXT -1 44 "Permission is granted to use and modify for " }}{PARA 0 "
" 0 "" {TEXT -1 37 "academic and non-commercial purposes." }}{PARA 0 "
" 0 "" {TEXT -1 13 "Dr. John Pais" }}{PARA 0 "" 0 "" {TEXT -1 28 "Math
ematics Department-MICDS" }}{PARA 0 "" 0 "" {TEXT -1 45 "E-mail: pais@
micds.org or pais@kinetigram.com" }}{PARA 0 "" 0 "" {TEXT -1 33 "URL: \+
 http://kinetigram.com/micds" }}{PARA 0 "" 0 "" {TEXT -1 37 "_________
____________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
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