正确绘制二次函数

Question

我有以下 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}

问题是第一个坐标应该是 (-1,10)，但我的代码绘制的是 (-1,8)。其他点似乎没问题。函数是 y=x²-5x+4

请告知，我的请求如下：

1. 帮助我修正此代码，以便图形能够按应有的方式通过 (-1,10)，而不是 (-1,8)
2. 如果标签（y=x²-5x+4）倾斜并沿着曲线而不是悬挂在顶部，我会很高兴。

Answer 1

问题的根源\x^2在于您的功能。正确答案是(\x)^2。

尝试：

\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}

Answer 2

这是另一种解决方案pgfplots，我没有改变你的情节命令。

输出

代码

\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}