I have a plot of the parabola `y = x^{2} - 5x + 4` over the interval `[-2, 7]` and a normal line to it. I have grid lines spaced the default 5 units apart. Since the parabola and the line intersect at `(4,0)`, I have `extra x ticks={4}` in the code to mark it, and I have `extra x tick labels={$\scriptstyle4$}` to label it. An extra vertical grid line is plotted there. How do I remove it?

I like the lengths that I have for the `x`-axis and `y`-axis. The grid lines are drawn too long. If I reduce the values for `xmin`, `xmax`, `ymin`, or `ymax`, the grid lines are shortened as well as the axes. How do I just shorten the grid lines?

Also, I don't like the display for labeling the vertex. If I label the vertex, I want to express the coordinates as fractions. Does anyone have a suggestion?

```
\documentclass[10pt]{amsart}
\usepackage{mathtools}

\usepackage{tikz}
\usetikzlibrary{calc,intersections}

\usepackage{pgfplots}
\pgfplotsset{compat=1.11}

\begin{document}

\begin{tikzpicture}
\begin{axis}[width=4in,grid=both,grid style={line width=.1pt, draw=gray!25}, axis equal image, clip=false,
    axis lines=middle,
    xmin=-7.5,xmax=12.5,
    ymin=-7,ymax=22.5,
    restrict y to domain=-5:20,
    xticklabels={, , , , , ,},
    yticklabels={, , , , , , ,},
    extra x ticks={4},
    extra x tick style={xticklabel style={font=\tiny,fill=white, circle, inner sep=1.5pt}},
    extra x tick labels={$\scriptstyle4$},
    axis line style={latex-latex},
    axis line style={shorten >=-7.5pt, shorten <=-7.5pt},
    xlabel=$x$, ylabel=$y$,
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
]

\addplot[samples=501, domain=-2:7] {x^2 - 5*x + 4} node[anchor=west, pos=1, font=\footnotesize]{$y=x^{2}-5x+4$};
\addplot[samples=2, domain=-7.5:12.5, latex-latex] {(-1/3)*x + 4/3} node[anchor=east, pos=0, font=\footnotesize]{$y=-\dfrac{1}{3}x+\dfrac{4}{3}$};

\draw[fill] (4,0) circle [radius=1.5pt];
\draw[fill] (2.5,-2.25) circle [radius=1.5pt];
\node[anchor=north, inner sep=0, font=\tiny] at (2.5,-2.5){$\left(\dfrac{5}{2}, -\dfrac{9}{4}\right)$};

\end{axis}
\end{tikzpicture}

\end{document}

```