\begin{tikzpicture}
[line cap=round,line join=round,x=1cm,y=1cm]
\tikzset{
        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
        small dot/.style={fill=black,circle,scale=0.3},}
\begin{axis}[
x=2cm,y=2cm,
axis lines=middle,
axis line style = {-latex},
xmin=-0.75,
xmax=3.75,
ymin=-0.5,
ymax=3.5,
ytick=\empty,
xtick=\empty,
xlabel=$x$,
ylabel=$y$,
extra x ticks={0.75, 2, 2.5,2.8},
extra x tick labels={$x_1$, $x_3$, $x_0$, $x_2$},
extra y ticks={0.64, 1.5, 2.0625, 2.46},
extra y tick labels={$f(x_1)$, $f(x_3)$, $g$ , $f(x_2)$},
]

\addplot[domain=0.5:3.1, blue, line width=1,samples=500] {0.25*(x^2)+0.5};


\draw [line width=0.1] (axis cs: 0.75,-0.05) -- (axis cs: 0.75,0.640625);
\draw [line width=0.1] (axis cs: -0.05,0.640625) -- (axis cs: 0.75,0.640625);

\draw [ultra thin] (axis cs: 2,-0.05) -- (axis cs: 2,1.5);
\draw [ultra thin] (axis cs: -0.05,1.5) -- (axis cs: 2,1.5);

\draw [loosely dashed, ultra thin] (axis cs: 2.5,-0.05) -- (axis cs: 2.5,2.0625);
\draw [loosely dashed, thin] (axis cs: -0.05,2.0625) -- (axis cs: 2.5,2.0625);

\draw [ultra thin] (axis cs: 2.8,-0.05) -- (axis cs: 2.8,2.46);
\draw [ultra thin] (axis cs: -0.05,2.46) -- (axis cs: 2.8,2.46);


\addplot[color=blue!80!black, only marks, style={mark=*}] coordinates {(0.75,0.640625)};
\addplot[color=blue!80!black, only marks, style={mark=*}] coordinates {(2,1.5)};

\addplot[color=blue, only marks, fill=white] coordinates {(2.5,2.0625)};

\addplot[color=blue!80!black, only marks, style={mark=*}] coordinates {(2.8,2.46)};


\node () at (axis cs:2.5,2.8) {$\displaystyle y=\left(x\right)$};

\end{axis}


\end{tikzpicture}