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{SECT 0 {EXCHG {PARA 18 "" 0 "top_s05_3" {TEXT -1 25 "5.3  Designer Po
lynomials" }}{PARA 19 "" 0 "" {TEXT -1 25 "Art Belmonte, Summer 1996" 
}}{PARA 0 "" 0 "" {TEXT -1 119 "These are the shaded gray examples whi
ch appear in Section 5.3. In-line plots have been removed to conserve \+
disk space." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "restart; f:=
x->a*x^3 + b*x^2 + c*x + d;\neq1:=f(-2)=0; eq2:=f(3)=4;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"fG:6#%\"xG6\"6$%)operatorG%&arrowGF(,**&%\"a
G\"\"\"9$\"\"$F/*&%\"bGF/F0\"\"#F/*&%\"cGF/F0F/F/%\"dGF/F(F(" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$eq1G/,*%\"aG!\")%\"bG\"\"%%\"cG!\"#%\"dG
\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq2G/,*%\"aG\"#F%\"b
G\"\"*%\"cG\"\"$%\"dG\"\"\"\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "eq3:=D(f)(-2)=0; eq4:=D(f)(3)=0;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$eq3G/,(%\"aG\"#7%\"bG!\"%%\"cG\"\"\"\"\"!" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$eq4G/,(%\"aG\"#F%\"bG\"\"'%\"cG\"\"\"\"\"
!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "sol:=solve(\{eq.(1..4)
\}, \{a, b, c, d\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$solG<&/%\"a
G#!\")\"$D\"/%\"cG#\"$W\"F*/%\"dG#\"$w\"F*/%\"bG#\"#7F*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "g:=subs(sol, f(x));" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"gG,**$%\"xG\"\"$#!\")\"$D\"*$F'\"\"##\"#7F+F'#
\"$W\"F+#\"$w\"F+\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Yes, t
his checks out!" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "p
lot(g, x=-3..4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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