Help with plotting Quadratics in pgfplots

Question

I'm practically new to the pgfplots package. I want to plot the quadratic equation 2x²-5x+2 on a set of axes (this is for an A-level text book). I have two questions:

1. Why does plotting x² in the domain [-2.5,2,5] result in the negative part being rotated 180°? This code:

   \documentclass{minimal}
   \usepackage{tikz,pgfplots}
   \begin{document}
      \begin{center}
       \begin{tikzpicture}
       @Axes
       \draw (0.1,-0.2) node[left]{\textcolor{gray}{O}};   
       \draw[thick, color=gray,->] (-5,0) -- (5,0) node[right] {\textcolor{black}{$x$}};
       \draw[thick, color=gray, ->] (0,-1) -- (0,7) node[above] {\textcolor{black}{$f(x)$}};
   
       @Plot
       \draw [red, thick, domain=-2.5:2.5, samples=100] plot(\x, {\x^2});
       \end{tikzpicture}
      \end{center}
   \end{document}
   

   Outputs:

2. Why does changing the equation to 2x²-5x+2 in the above equation; i.e. writing plot(\x, {2\x^2-5\x+2}); not output my axes at all, but instead outputs these two pages?

Any help will be greatly appreciated.

Answer 1

Since you're loading pgfplots, why not use it's features. As mentioned in a few comments, you're not actually using it. Then you get automatic scaling, and you don't need to enclose x in parenthesis to get the correct result.

\documentclass{article}
\usepackage{pgfplots}
\begin{document}
\begin{center}
  \begin{tikzpicture}
  \begin{axis}[
      % width and height if axis, adjust to your liking
      width=7cm,
      height=6cm,
      xtick=\empty, % remove all ticks from x-axis
      ytick=\empty, % ditto for y-axis
      xlabel=$x$, 
      ylabel=$y$,
      axis lines=center, % default is to make a box around the axis
      domain=-2.5:2.5,
      samples=100]
    \addplot [red] {x^2};
    \addplot [blue] {2*x^2 + 5*x + 2};
  \end{axis}
  \end{tikzpicture}
\end{center}
\end{document}