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\usepackage{ascmac,bm,amssymb}
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\usepackage{graphicx,color}
%\usepackage{qrcode}
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\usetikzlibrary{calc}
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\textwidth=330truemm \textheight=226truemm \columnseprule=0pt
\topmargin=-24truemm \oddsidemargin=-8truemm

\hypersetup{% Oct 1 2023
	pdftitle={数学授業プリント},
	pdfauthor={gbb60166@gmail.com},
	pdfsubject={https://unilab.gbb60166.jp/math_ia/math_ia.htm}
	}

\newenvironment{nidan}{\begin{minipage}[t]{.225\textwidth}}{\end{minipage}}
%\def\nidangumi#1#2{\begin{nidan}{#1}\end{nidan}\quad%
%\begin{nidan}{#2}\end{nidan}}
\newcommand{\nidangumi}[2]{\begin{nidan}{#1}\end{nidan}\quad%
\begin{nidan}{#2}\end{nidan}}

% ■■■ 0より大きいときはdvipdfmxで印刷用PDFを作ることを想定（答えはプリント
% 下部に出力される）
%        0 のときはdvipdfmxでデジタル教材用PDFを作ることを想定（答えは問題の
% すぐ横に赤で出力され、後でOneNoteで黒く塗りつぶし）
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\everymath{\displaystyle}
\parindent=0zw \columnsep=3zw
\lineskiplimit=1ex \normallineskiplimit=\lineskiplimit 
\lineskip=\lineskiplimit \normallineskip=\lineskiplimit

\newcounter{toi} \newcounter{subtoi}[toi]
\newcounter{subsubtoi}[subtoi]

\def\toi{\refstepcounter{toi}\par          % 問
  \makebox[2zw][r]{\Large\ajKaku{\value{toi}}\hspace{0.5zw}}%
  \hangindent=2zw}

\def\subtoi{\refstepcounter{subtoi}\par    % 小問
  \makebox[3.4zw][r]{\ajKakko{\value{subtoi}}\hspace{1zw}}%
  \hangindent=3.4zw}

\def\subsubtoi{\refstepcounter{subsubtoi}\par    % 小小問
  \makebox[4.2zw][r]{\ajMaru{\value{subtoi}}\hspace{1zw}}%
  \hangindent=4.2zw}

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	\def\kotae#1{\hfill \textcolor{red}{\footnotesize\gtfamily\bfseries\(\boldsymbol{#1} \)}}
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\makeatletter
\def\hooklen#1#2{\settowidth{\@tempdima}{\(#1\)}
%\advance\@tempdima by.3ex
% ↑ 数式モードで式の前後に入るスペースを制御したかったが、
%    難しいのでやめた。段々難解なコードになっているのでやめた方がよい？
\hbox to\@tempdima{\hfil \(#2\)\hfil}}
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\begin{document}
%
%  ===========================以下本文===============================
%
\def\namae{%
{\Large\gtfamily\bfseries 数学I \quad 授業プリント \# 38（その2）}\hfill
年\hskip8ex 組\hskip8ex 号 \hskip5ex

\hfill 
\underline{氏名\rule[-2ex]{0cm}{6ex}\hskip30ex}}

\namae

\vskip-2ex

{\large\gtfamily\bfseries ■　2次関数のグラフと2次方程式}

\def\arraystretch{1.5}
\def\mb#1{\makebox[3ex]{#1}}
\def\bbox{\raisebox{-1.5ex}{\framebox(7,7){}}}
\unitlength=1mm

\def\siki{y=x^2-4x+3}

\fbox{例題1}　
\begin{minipage}[t]{0.28\textwidth}
　\( \siki \) のグラフをかくと次のようになり，$x$軸と2点で交わる。

　このときグラフと$x$軸との交点の$y$座標は0だから，交点の$x$座標を求める
には\(y=x^2-4x+3\)で$y=0$とおいた式，つまり「\(x^2-4x+3=0\)」を解けば
良い。

\bigskip

\hspace*{8zw}\(x^2-4x+3=0\)

因数分解して\hskip1zw \((x-1)(x-3)=0\)

\hspace*{10zw}\(x=1,3\)

\end{minipage}


\vskip-10zh
\mbox{}\hfill
\begin{tikzpicture}[scale=0.6, >=stealth, baseline=(current bounding box.north)]
\draw[->](-1,0) -- (5,0);
\draw[->](0,-1) -- (0,4);
%\foreach \x in {-4,...,4}{\foreach \y in {-6,...,6}{\fill (\x,\y) circle (2pt);}}
\draw(-0.3,-0.3) node {\footnotesize O};
\draw(5,-0.3) node {\footnotesize $x$};
\draw(-0.3,4) node {\footnotesize $y$};
%\foreach \x in {5,-5}{\draw(-0.3,\x) node {\tiny $\x$};}
%\draw(5,-0.3) node {\tiny $5$};
\draw($ (-0.2,{(-0.2)^2-4*(-0.2)+3}) $) parabola bend (2,-1) (4,3);
\foreach \x in {1,...,4}{\draw(\x,-0.05)--(\x,0.05);}
\foreach \x in {1,...,4}{\draw(-0.05,\x)--(0.05,\x);}
%\draw(-1.2,-0.5) node {\tiny \( \scriptstyle {3-\sqrt{17}\over 4} \)};
%\draw(2.5,-0.5) node {\tiny \( \scriptstyle {3+\sqrt{17}\over 4} \)};
\end{tikzpicture}


\vspace*{8mm}

\begin{center}
\begin{minipage}[t]{0.4\textwidth}
\begin{shadebox}
\vspace*{1ex}

\hspace*{7zw}\fbox{\begin{minipage}[c]{9zw}
\(y=ax^2+bx+c\)\\
のグラフと$x$軸との\\
交点の$x$座標
\end{minipage}}
\quad {\LARGE\(=\)} \quad
\fbox{\begin{minipage}[c]{8zw}
2次方程式\\
\(ax^2+bx+c=0\)\\
の解
\end{minipage}}

\vspace*{1ex}

\end{shadebox}
\end{minipage}
\end{center}


\toi 次の2次関数のグラフと$x$軸との交点の$x$座標を
求めなさい。

\nidangumi{\subtoi \( y=x^2+4x+3 \)\kotae{x=-3,-1} }
			{\subtoi  \(  y=x^2-3x+2 \)\kotae{x=1,2} }

\vskip-1zh
\hspace*{45mm}
\begin{tikzpicture}[scale=0.6, >=stealth, baseline=(current bounding box.north)]
\draw[->](-5,0) -- (1,0);
\draw[->](0,-1) -- (0,4);
%\foreach \x in {-4,...,4}{\foreach \y in {-6,...,6}{\fill (\x,\y) circle (2pt);}}
\draw(-0.3,-0.3) node {\footnotesize O};
\draw(1,-0.3) node {\tiny $x$};
\draw(-0.3,4) node {\tiny $y$};
%\foreach \x in {5,-5}{\draw(-0.3,\x) node {\tiny $\x$};}
%\draw(5,-0.3) node {\tiny $5$};
\draw($ (-4.1,{(-4.1)^2+4*(-4.1)+3}) $) parabola bend (-2,-1) ($ (0.1,{(0.1)^2+4*(0.1)+3}) $);
\foreach \x in {-5,...,-1}{\draw(\x,-0.05)--(\x,0.05);}
\foreach \x in {1,...,3}{\draw(-0.05,\x)--(0.05,\x);}
%\draw(-1.2,-0.5) node {\tiny \( \scriptstyle {3-\sqrt{17}\over 4} \)};
%\draw(2.5,-0.5) node {\tiny \( \scriptstyle {3+\sqrt{17}\over 4} \)};
\end{tikzpicture}
%
\hspace*{45mm}
%
\begin{tikzpicture}[scale=0.6, >=stealth, baseline=(current bounding box.north)]
\draw[->](-1,0) -- (3,0);
\draw[->](0,-1) -- (0,4);
%\foreach \x in {-4,...,4}{\foreach \y in {-6,...,6}{\fill (\x,\y) circle (2pt);}}
\draw(-0.3,-0.3) node {\footnotesize O};
\draw(3,-0.3) node {\tiny $x$};
\draw(-0.3,4) node {\tiny $y$};
%\foreach \x in {5,-5}{\draw(-0.3,\x) node {\tiny $\x$};}
%\draw(5,-0.3) node {\tiny $5$};
%\draw ($ (-1,{2*(-1)^2-3*(-1)-1}) $) parabola bend ($ ({-(b)/(2*a)},{(-(b)^2+4*a*(c))/(4*a)}) $) ($ (2.5,{2*(2.5)^2-3*(2.5)-1}) $);
\draw($ (-0.2,{(-0.2)^2-3*(-0.2)+2}) $) parabola bend (1.5,-0.25) ($ (3.2,{(3.2)^2-3*(3.2)+2}) $);
\foreach \x in {1,...,2}{\draw(\x,-0.05)--(\x,0.05);}
\foreach \x in {1,...,3}{\draw(-0.05,\x)--(0.05,\x);}
%\draw(-1.2,-0.5) node {\tiny \( \scriptstyle {3-\sqrt{17}\over 4} \)};
%\draw(2.5,-0.5) node {\tiny \( \scriptstyle {3+\sqrt{17}\over 4} \)};
\end{tikzpicture}



\vfill

\nidangumi{\subtoi \( y=x^2+3x-10 \)\kotae{x=-5,2} }
			{\subtoi  \(  y=x^2+x  \)\kotae{x=0,-1} }

\vskip-1zh
\hspace*{50mm}
\begin{tikzpicture}[scale=0.25, >=stealth, baseline=(current bounding box.north)]
\draw[->](-6,0) -- (3,0);
\draw[->](0,-12) -- (0,2);
%\foreach \x in {-4,...,4}{\foreach \y in {-6,...,6}{\fill (\x,\y) circle (2pt);}}
\draw(-1,-1) node {\footnotesize O};
\draw(3,-1) node {\tiny $x$};
\draw(-1,2) node {\tiny $y$};
%\foreach \x in {5,-5}{\draw(-0.3,\x) node {\tiny $\x$};}
%\draw(5,-0.3) node {\tiny $5$};
%\draw ($ (-1,{2*(-1)^2-3*(-1)-1}) $) parabola bend ($ ({-(b)/(2*a)},{(-(b)^2+4*a*(c))/(4*a)}) $) ($ (2.5,{2*(2.5)^2-3*(2.5)-1}) $);
\draw($ (-5.2,{(-5.2)^2+3*(-5.2)-10}) $) parabola bend ($ ({-(3)/(2*1)},{(-(3)^2+4*1*(-10))/(4*1)}) $) ($ (2.2,{(2.2)^2+3*(2.2)-10}) $);
\foreach \x in {-5,...,2}{\draw(\x,-0.05)--(\x,0.05);}
\foreach \x in {-11,...,1}{\draw(-0.05,\x)--(0.05,\x);}
%\draw(-1.2,-0.5) node {\tiny \( \scriptstyle {3-\sqrt{17}\over 4} \)};
%\draw(2.5,-0.5) node {\tiny \( \scriptstyle {3+\sqrt{17}\over 4} \)};
\end{tikzpicture}
%
\hspace*{55mm}
%
\begin{tikzpicture}[scale=0.6, >=stealth, baseline=(current bounding box.north)]
\draw[->](-2,0) -- (2,0);
\draw[->](0,-1) -- (0,3);
%\foreach \x in {-4,...,4}{\foreach \y in {-6,...,6}{\fill (\x,\y) circle (2pt);}}
\draw(0.3,-0.3) node {\footnotesize O};
\draw(2,-0.3) node {\tiny $x$};
\draw(-0.3,3) node {\tiny $y$};
%\foreach \x in {5,-5}{\draw(-0.3,\x) node {\tiny $\x$};}
%\draw(5,-0.3) node {\tiny $5$};
\draw($ (-2.3,{(-2.3)^2+(-2.3)}) $) parabola bend ($ ({-1/2},{-1/4}) $) ($ (1.3,{(1.3)^2+(1.3)}) $);
\foreach \x in {-1,...,1}{\draw(\x,-0.05)--(\x,0.05);}
\foreach \x in {1,...,2}{\draw(-0.05,\x)--(0.05,\x);}
%\draw(-1.2,-0.5) node {\tiny \( \scriptstyle {3-\sqrt{17}\over 4} \)};
%\draw(2.5,-0.5) node {\tiny \( \scriptstyle {3+\sqrt{17}\over 4} \)};
\end{tikzpicture}



\vfill



\ifnum\make_pdf_with_insatsu>0
	\hfill\rotatebox{180}{\scriptsize
	{\normalsize\ajKaku{3}} \ajKakko{1}~$x=-{1\over2},-3$ \ 
	\ajKakko{2}~$x=-{1\over2},-1$ \ 
	\ajKakko{3}~$x=-{4\over3},2$ \ \ajKakko{4}~$x={5\pm\sqrt{17}\over2}$ \ 
	\ajKakko{5}~$x={1\over3},2$ \ \ajKakko{6}~$x={1\over6},-{1\over2}$ \ 
	\ajKakko{7}~$x={-5\pm\sqrt{105}\over4}$ \ 
	\ajKakko{8}~$x={1\pm\sqrt{33}\over4}$ \ 
	\ajKakko{9}~$x={1\pm\sqrt{17}\over4}$ \ 
	\ajKakko{10}~$x=-{1\over2},-2$ \ 
	\ajKakko{11}~$x={9\pm\sqrt{101}\over10}$ \ 
	\ajKakko{12}~$x=0,3$ \ \ajKakko{13}~$x={2\over3},3$ \ 
	\ajKakko{14}~$x={9\pm\sqrt{21}\over6}$ \ 
	\ajKakko{15}~$x=\pm2$ \ \ajKakko{16}~$x={3\pm\sqrt{3}\over2}$
	}
\fi


\newpage%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\def\siki{2x^2-3x-1}

\fbox{例題2}　
\begin{minipage}[t]{0.5\textwidth}
　\( y=\siki \) のグラフと$x$軸との交点の$x$座標を
求めなさい。
\end{minipage}

\bigskip


\hskip1.8zw\fbox{解}
\begin{minipage}[t]{0.28\textwidth}
　\(\siki\)は因数分解出来ないので，\\
解の公式\(x={-b\pm\sqrt{b^2-4ac}\over 2a }\)を使う。

\bigskip

\(\siki=0\)を解の公式で解くと

\(a=2,~~b=-3,~~c=-1\)だから

\hspace*{3zw}\(x={-b\pm\sqrt{b^2-4ac}\over 2a }\)

\hspace*{3.8zw}\(={-(-3)\pm\sqrt{(-3)^2-4\times2\times(-1)}\over 2\times2 }\)

\hspace*{3.8zw}\(={3\pm\sqrt{9+8}\over 4}\)

\hspace*{3.8zw}\(={3\pm\sqrt{17}\over 4}\)

\bigskip

%よってグラフは右のようになるので，
%
%\hspace*{5zw} 〈答〉 \({3-\sqrt{17}\over 4}≦x≦{3+\sqrt{17}\over 4}\)


\end{minipage}

\vskip-22zh
\mbox{}\hspace*{25zw}
\begin{tikzpicture}[scale=0.6, >=stealth, baseline=(current bounding box.north)]
\draw[->](-3,0) -- (4,0);
\draw[->](0,-2) -- (0,5);
%\foreach \x in {-4,...,4}{\foreach \y in {-6,...,6}{\fill (\x,\y) circle (2pt);}}
\draw(0.3,-0.3) node {\footnotesize O};
\draw(4,-0.3) node {\footnotesize $x$};
\draw(-0.3,5) node {\footnotesize $y$};
%\foreach \x in {5,-5}{\draw(-0.3,\x) node {\tiny $\x$};}
%\draw(5,-0.3) node {\tiny $5$};
%\draw ($ (-1,{2*(-1)^2-3*(-1)-1}) $) parabola bend ($ ({-(b)/(2*a)},{(-(b)^2+4*a*(c))/(4*a)}) $) ($ (2.5,{2*(2.5)^2-3*(2.5)-1}) $);
\draw ($ (-1,{2*(-1)^2-3*(-1)-1}) $) parabola bend ($ ({-(-3)/(2*2)},{(-(-3)^2+4*2*(-1))/(4*2)}) $) ($ (2.5,{2*(2.5)^2-3*(2.5)-1}) $);
\foreach \x in {-2,...,3}{\draw(\x,-0.05)--(\x,0.05);}
\foreach \x in {-1,...,4}{\draw(-0.05,\x)--(0.05,\x);}
\draw(-1.2,-0.5) node {\tiny \( \scriptstyle {3-\sqrt{17}\over 4} \)};
\draw(2.5,-0.5) node {\tiny \( \scriptstyle {3+\sqrt{17}\over 4} \)};
\end{tikzpicture}

\vskip9zh

\toi 次の2次関数のグラフと$x$軸との交点の$x$座標を
求めなさい。


\nidangumi{\subtoi \( y=x^2-3x+1 \)\kotae{x={3\pm\sqrt{5}\over2}}}
	{\subtoi \( y=x^2-3x-2 \)\kotae{x={3\pm\sqrt{17}\over2}}}\vfill

\nidangumi{\subtoi \( y=2x^2-3x-4 \)\kotae{x={3\pm\sqrt{41}\over4}}}
	{\subtoi \( y=x^2-x-3 \)\kotae{x={1\pm\sqrt{13}\over2}}}\vfill



\newpage


\toi 次の2次関数のグラフと$x$軸との交点の$x$座標を
求めなさい。

\nidangumi{\subtoi \( y=2x^2+7x+3 \)\kotae{x=-{1\over2},-3}}%因数分解タイプ
	{\subtoi \( y=2x^2+3x+1 \)\kotae{x=-{1\over2},-1}}\vfill%因数分解タイプ

\nidangumi{\subtoi \( y=3x^2-2x-8 \)\kotae{x=-{4\over3},2}}%因数分解タイプ
	{\subtoi \( y=x^2-5x+2 \)\kotae{x={5\pm\sqrt{17}\over2}}}\vfill

\nidangumi{\subtoi \( y=3x^2-7x+2 \)\kotae{x={1\over3},2}}%因数分解タイプ
	{\subtoi \( y=12x^2+4x-1 \)\kotae{x={1\over6},-{1\over2}}}\vfill%因数分解タイプ

\nidangumi{\subtoi \( y=2x^2+5x-10 \)\kotae{x={-5\pm\sqrt{105}\over4}}}
	{\subtoi \( y=2x^2-x-4 \)\kotae{x={1\pm\sqrt{33}\over4}}}\vfill



\ifnum\make_pdf_with_insatsu>0
	\hfill\rotatebox{180}{{\normalsize\gtfamily\bfseries プリント\#38（その2）}
	\scriptsize
	{\normalsize\ajKaku{1}} \ajKakko{1}~\( x=-3,-1 \) \ 
	\ajKakko{2}~\( x=1,2 \) \ \ajKakko{3}~\( x=-5,2 \) \ 
	\ajKakko{4}~\( x=0,-1 \) \ 
	{\normalsize\ajKaku{2}} \ajKakko{1}~\( x={3\pm\sqrt{5}\over2} \) \ 
	\ajKakko{2}~\( x={3\pm\sqrt{17}\over2} \) \ 
	\ajKakko{3}~\( x={3\pm\sqrt{41}\over4} \) \ 
	\ajKakko{4}~\( x={1\pm\sqrt{13}\over2} \)
	}
\fi


\newpage


\nidangumi{\subtoi \( y=2x^2-x-2 \)\kotae{x={1\pm\sqrt{17}\over4}}}
	{\subtoi \( y=2x^2+5x+2 \)\kotae{x=-{1\over2},-2}}\vfill%因数分解タイプ

\nidangumi{\subtoi \( y=5x^2-9x-1 \)\kotae{x={9\pm\sqrt{101}\over10}}}
	{\subtoi \( y=x^2-3x \)\kotae{x=0,3}}\vfill%因数分解タイプ

\nidangumi{\subtoi \( y=3x^2-11x+6 \)\kotae{x={2\over3},3}}%因数分解タイプ
	{\subtoi \( y=3x^2-9x+5 \)\kotae{x={9\pm\sqrt{21}\over6}}}\vfill

\nidangumi{\subtoi \( y=x^2-4 \)\kotae{x=\pm2}}%因数分解タイプ
	{\subtoi \( y=2x^2-6x+3 \)\kotae{x={3\pm\sqrt{3}\over2}}}\vfill

\end{document}
