# LaTeX2HTML 2002 (1.62)
# Associate images original text with physical files.


$key = q/displaystylefrac{p}{2}=frac{1}{4a};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$\displaystyle\frac{p}{2}=\frac{1}{4a}$">|; 

$key = q/X=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$X=0$">|; 

$key = q/{displaymath}left(y+frac{10}{3}right)=3left(x+frac{1}{3}right)^2{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="\begin{displaymath}
\left(y+\frac{10}{3}\right)=3\left(x+\frac{1}{3}\right)^2
\end{displaymath}">|; 

$key = q/x=-displaystylefrac{1}{3};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$x=-\displaystyle\frac{1}{3}$">|; 

$key = q/{displaymath}left{array{{c}2ah+b=0ah^2+bh+c-k=0array{right.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="\begin{displaymath}
\left\{
\begin{array}{c}
2ah+b=0\\\\
ah^2+bh+c-k=0
\end{array}
\right.
\end{displaymath}">|; 

$key = q/x=ay^2+by+c;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$x=ay^2+by+c$">|; 

$key = q/{displaymath}Y=aX^2+X(2ah+b)+(ah^2+bh+c-k).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="341" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="\begin{displaymath}
Y=aX^2+X(2ah+b)+(ah^2+bh+c-k).
\end{displaymath}">|; 

$key = q/F=(0,displaystylefrac{p}{2})=(0,displaystylefrac{1}{12});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$F=(0,\displaystyle\frac{p}{2})=(0,\displaystyle\frac{1}{12})$">|; 

$key = q/x;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$x$">|; 

$key = q/displaystyleF=left(-frac{b}{2a},frac{4ac-b^2+1}{4a}right);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$\displaystyle F=\left(-\frac{b}{2a},\frac{4ac-b^2+1}{4a}\right)$">|; 

$key = q/X=0,Y=displaystylefrac{p}{2}=frac{1}{4a};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$X=0, Y=\displaystyle\frac{p}{2}=\frac{1}{4a}$">|; 

$key = q/X,Y;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$X, Y$">|; 

$key = q/{displaymath}displaystyley=3left(x^2+frac{2}{3}x+frac{1}{9}right)-3-frac{1}{3}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="\begin{displaymath}
\displaystyle
y=3\left(x^2+\frac{2}{3}x+\frac{1}{9}\right)-3-\frac{1}{3}
\end{displaymath}">|; 

$key = q/x,y;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$x,y$">|; 

$key = q/displaystyleV=left(-frac{b}{2a},frac{4ac-b^2}{4a}right);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$\displaystyle
V=\left(-\frac{b}{2a},\frac{4ac-b^2}{4a}\right)$">|; 

$key = q/displaystyleV=left(frac{4ac-b^2}{4a},-frac{b}{2a}right);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$\displaystyle V=\left(\frac{4ac-b^2}{4a},-\frac{b}{2a}\right)$">|; 

$key = q/X=Y=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$X=Y=0$">|; 

$key = q/y=ax^2+bx+c;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$y=ax^2+bx+c$">|; 

$key = q/{displaymath}left{array{{c}h=-displaystylefrac{b}{2a}vspace{1mm}k=ah^2+bh+carray{right.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="90" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="\begin{displaymath}
\left\{
\begin{array}{c}
h=-\displaystyle\frac{b}{2a}\\\\
\vspace{1mm}\\\\
k=ah^2+bh+c
\end{array}
\right.
\end{displaymath}">|; 

$key = q/{displaymath}left{array{{c}x=X+hy=Y+karray{right.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="\begin{displaymath}
\left\{
\begin{array}{c}
x=X+h\\\\
y=Y+k
\end{array}
\right.
\end{displaymath}">|; 

$key = q/mathcal{C}:y=3x^{2}+2x-3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$\mathcal{C}:y=3x^{2}+2x-3$">|; 

$key = q/Y=-displaystylefrac{1}{12};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$Y=-\displaystyle\frac{1}{12}$">|; 

$key = q/displaystyleF=(X-frac{1}{3},Y-frac{10}{3})=(-frac{1}{3},-frac{39}{12});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="274" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$\displaystyle F=(X-\frac{1}{3},Y-\frac{10}{3})=(-\frac{1}{3},-\frac{39}{12})$">|; 

$key = q/{displaymath}con,,,a,b,cinmathbf{R},,,aneq0{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="\begin{displaymath}
con   a,b,c \in\mathbf{R},   a\neq0
\end{displaymath}">|; 

$key = q/{displaymath}left{array{{c}displaystylex=X-frac{b}{2a}vspace{2mm}displaystyley=Y+frac{4ac-b^2}{4a}array{right.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="135" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="\begin{displaymath}
\left\{
\begin{array}{c}
\displaystyle x=X-\frac{b}{2a...
...
\displaystyle y=Y+\frac{4ac-b^2}{4a}
\end{array}
\right.
\end{displaymath}">|; 

$key = q/Y;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$Y$">|; 

$key = q/y;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$y$">|; 

$key = q/V=(0,0);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$V=(0,0)$">|; 

$key = q/{displaymath}y=ax^2+bx+c{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="\begin{displaymath}
y=ax^2+bx+c\\\\
\end{displaymath}">|; 

$key = q/displaystyled:y=frac{4ac-b^2-1}{4a};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$\displaystyle d:y=\frac{4ac-b^2-1}{4a}$">|; 

$key = q/Y=aX^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$Y=aX^2$">|; 

$key = q/Y=3X^2,p=displaystylefrac{1}{6};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$Y=3X^2,p=\displaystyle\frac{1}{6}$">|; 

$key = q/displaystyleF=left(frac{4ac-b^2+1}{4a},-frac{b}{2a}right);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$\displaystyle F=\left(\frac{4ac-b^2+1}{4a},-\frac{b}{2a}\right)$">|; 

$key = q/y=-displaystylefrac{41}{12};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$y=-\displaystyle\frac{41}{12}$">|; 

$key = q/{displaymath}left{array{{c}X=x+displaystylefrac{1}{3}vspace{2mm}Y=y+displaystylefrac{10}{3}array{right.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="86" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="\begin{displaymath}
\left \{
\begin{array}{c}
X=x+\displaystyle\frac{1}{3}\vs...
...{2mm}\\\\
Y=y+\displaystyle\frac{10}{3}
\end{array}
\right.
\end{displaymath}">|; 

$key = q/displaystylea=frac{1}{2p};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$\displaystyle a= \frac{1}{2p}$">|; 

$key = q/{displaymath}Y+k=a(X+h)^{2}+b(X+h)+c{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="264" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="\begin{displaymath}
Y+k=a(X+h)^{2}+b(X+h)+c
\end{displaymath}">|; 

$key = q/a=3,b=2,c=-3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$a=3, b=2, c=-3$">|; 

$key = q/V=(-displaystylefrac{1}{3},-displaystylefrac{10}{3});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$V=(-\displaystyle\frac{1}{3},-\displaystyle\frac{10}{3})$">|; 

$key = q/displaystyled:x=frac{4ac-b^2-1}{4a};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$\displaystyle d:x=\frac{4ac-b^2-1}{4a}$">|; 

1;

