# Graphing correctly a quadratic function

I have the following MWE

\documentclass[tikz,border=2mm]{standalone}
\begin{document}
\begin{tikzpicture}[domain=-1:6]
\draw[very thin, color=green, step=0.2cm](-2,-3) grid (7,11);
\draw[color=cyan](-2,-3) grid (7,11);
\draw[->,ultra thick] (-2,0)--(7,0) node[below]{$x$};
\draw[->,ultra thick] (0,-3)--(0,11) node[left]{$y$};
\foreach \x in {-1,0,...,6}
\draw (\x cm, 1pt)--(\x cm,-1pt) node[anchor=north] {$\x$};
\foreach \y in {-2,-1,...,10}
\draw (1pt, \y cm)--(-1pt, \y cm) node[anchor=east] {$\y$};
\draw[color=black, thick] plot (\x,\x^2-5*\x+4) node[]{$y=x^2-5x+4$};
\end{tikzpicture}

\end{document}


The problem is that the first coordinate should have been (-1,10) but my code is plotting (-1,8). Other points appear to be okay. The function is y=x²-5x+4

Please, my requests are as follows:

1. Help me correct this code so that the graph would pass through (-1,10) as it should, instead of (-1,8)
2. I would be glad if the label (y=x²-5x+4) is sloped and along the curve instead of hanging on top. • Try \draw[color=black, thick] plot (\x,\x*\x-5*\x+4) instead \draw[color=black, thick] plot (\x,\x^2-5*\x+4) – minhthien_2016 Oct 24 at 7:52
• Or \draw[color=black, thick,smooth,samples=100] plot (\x,\x*\x-5*\x+4) node[]{$y=x^2-5x+4$}; – minhthien_2016 Oct 24 at 8:01
• Thank you so much. – Chika Odiliobi Oct 24 at 14:10
• @ChikaOdiliobi, if you liked answer, you can upvote it or even accept :-) – Zarko Oct 24 at 14:14

Here's an alternative solution with pgfplots, I haven't changed your plot command.

## Output ## Code

\documentclass[margin=10pt]{standalone}
\usepackage{pgfplots}

\pgfplotsset{compat=1.17}

\begin{document}
\begin{tikzpicture}
\begin{axis}[%
domain=-1:6,
yscale=2,
axis lines=middle,
xlabel={\large $x$},
ylabel={\large $y$},
xtick={-1,...,6},
ytick={-2,...,10},
ymin=-3,
ymax=11,
xmin=-2,
xmax=7,
grid=both,
grid style={line width=.1pt, green},
major grid style={line width=.2pt,cyan},
minor tick num=4,
tick style={draw=none},
extra x ticks={-2,6,7},
extra y ticks={-3,10,11},
extra x tick labels={},
extra y tick labels={},
extra x tick style={grid=both},
extra y tick style={grid=both},
]
\addplot[thick,smooth, cyan!50!green] (\x,\x^2-5*\x+4) node[]{$y=x^2-5x+4$};
\end{axis}
\end{tikzpicture}
\end{document}


Culprits of your problem is \x^2 in your function. Correct is (\x)^2.

Try:

\documentclass[tikz,border=2mm]{standalone}
\usetikzlibrary{arrows.meta}

\begin{document}
\begin{tikzpicture}[
arr/.style = {very thick, draw=gray, -{Straight Barb[length=1mm]}},
domain=-1:6, samples=70
]
\draw[very thin, color=green, step=0.2cm](-2,-3) grid (7,11);
\draw[color=cyan](-2,-3) grid (7,11);
\draw[arr] (-2,0) -- (7, 0) node[below]{$x$};
\draw[arr] (0,-3) -- (0,11) node[left]{$y$};
% tick labels
\foreach \x in {-1,0,...,6}
\draw (\x, 1pt) -- ++ (0,-1pt) node[below left] {$\x$};
\foreach \y in {-2,-1,...,10}
\draw (1pt, \y) -- ++ (-1pt, 0) node[below right] {$\y$};
% function
\draw[color=black, thick] plot (\x,{(\x)^2 - 5*\x+4})
node[anchor=north east, rotate=80] {$y=x^2-5x+4$};
\end{tikzpicture}

\end{document} • \usetikzlibrary{arrows.meta} need for Straight Barb[length=1mm]. – M.Ahmadi Oct 24 at 10:34
• @M.Ahmadi, you are right! This line was lost during updating of MWE ... :-(. Corrected now. – Zarko Oct 24 at 12:57
• Thank you very much – Chika Odiliobi Oct 24 at 14:11
• @Zarko the line node[xshift=1em, anchor=east, rotate=80] {$y=x^2-5x+4$}; could be improved by replacing the options with node[anchor=north east, below, sloped] {$y=x^2-5x+4$};, I think. – Alenanno Oct 24 at 14:33
• @Alenanno, checked. You are right. Corrected. Thank you very much! – Zarko Oct 24 at 14:39