Plotting function graphs with LaTeX

pdflatex latex.tex -output-format=pdf

\documentclass{article}

\usepackage{tikz}
\usepackage{pgfplots}

\begin{document}
    \begin{tikzpicture}
        \begin{axis}
            \addplot+[id=parable,domain=-5:5]
            gnuplot{4*x**2 - 5}
            node[pin=180:{$4x^2-5$}]{};
        \end{axis}
    \end{tikzpicture}
\end{document}

\documentclass{article}

\usepackage{tikz}

\begin{document}
    \begin{tikzpicture}
          \draw[very thin,color=gray] (0.0,0.0) grid (1.8,3.8);

          \draw[->] (-0.5,0) -- (2,0) node[right] {$x$};
          \draw[->] (0,-0.5) -- (0,4) node[above] {$y$};

          \draw [domain=0:1/3,red] plot (\x,3*3*\x);
          \draw [domain=1/3:2/3,red] plot (\x,2*3-3*3*\x);
          \draw [domain=2/3:1.5,red] plot (\x,0);

          \draw [domain=0:1/4,orange] plot (\x,4*4*\x);
          \draw [domain=1/4:2/4,orange] plot (\x,2*4-4*4*\x);
          \draw [domain=2/4:1.5,orange] plot (\x,0);
    \end{tikzpicture}
\end{document}

\documentclass{article}

\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{wrapfig}

\begin{document}
\begin{wrapfigure}{r}{.2\textwidth}
  \begin{center}
    \begin{tikzpicture}
          \draw[->] (-0.5,0) -- (2,0) node[right] {$x$};
          \draw[->] (0,-0.5) -- (0,4) node[above] {$y$};
          \draw [domain=0:1/3,red] plot (\x,3*3*\x);
          \draw [domain=1/3:2/3,red] plot (\x,2*3-3*3*\x);
          \draw [domain=2/3:1.5,red] plot (\x,0);

          \draw [domain=0:1/4,orange] plot (\x,4*4*\x);
          \draw [domain=1/4:2/4,orange] plot (\x,2*4-4*4*\x);
          \draw [domain=2/4:1.5,orange] plot (\x,0);
    \end{tikzpicture}
  \end{center}
\end{wrapfigure}

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\end{document}