Drawing parabola shape using Tikz

I had like to draw a general curve shape (kind of parabola) using Tikz.

I have managed to draw half circle as follows (black line):

\begin{figure}[htbp]
\centering
\begin{tikzpicture}[scale = 0.7]
\draw[thick,->] (0,0) -- (10,0) node[anchor=north west] {x};
\draw[thick,->] (0,0) -- (0,10) node[anchor=south east] {z};
\draw [dashed] (0,0) -- (3.5,3.5);
\draw [dashed] (3.5,3.5) -- (7,0);
\draw (7,0) arc (0:180:3.5);
\end{tikzpicture}
\caption{}
\end{figure}


However I had like to make a curve like the blue line.

Is there a way to do it?

Thank you

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{figure}[htbp]
\centering
% Note! if you change the scale = 2 to something else in the next line, you need to change the
% radius of the circles manually as well.
\begin{tikzpicture}[scale = 2]
% Axes
\draw[->, very thick] (0,0) -- (4.2,0) node[right] {$x$};       % X-axis
\draw[->, very thick] (0,0) -- (0,4.2) node[above] {$y$};   % Y-axis
% The plots
\draw[scale = 0.5, domain = 0:3, variable = \x, dash pattern = on 3pt off 1.5pt] plot ({\x}, {\x});         % left line
\draw[scale = 0.5, domain = 3:6, variable = \x, dash pattern = on 3pt off 1.5pt] plot ({\x}, {-\x + 6});    % right line
\draw[scale =0.15, domain = -4:4, variable = \x]  plot ({\x*3 +12},{-\x*\x + 16});                                  % parabola
% Labels
\fill (3.6,0)  circle[radius=1pt]node[anchor=north west] {$\alpha$};
\end{tikzpicture}
\caption{}
\end{figure}
\end{document}


\documentclass[tikz,border=3.14mm]{standalone}
\begin{document}
\begin{tikzpicture}[scale = 0.7]
\draw[thick,->] (0,0) -- (10,0) node[anchor=north west] {$x$};
\draw[thick,->] (0,0) -- (0,10) node[anchor=south east] {$z$};
\fill (0,0)  circle[radius=4pt] node[anchor=north west] {$M$};
\fill (7,0)  circle[radius=4pt] node[anchor=north west] {$T$};
\draw [dashed] (0,0) -- (3.5,3.5) -- (7,0);
\draw (7,0) arc (0:180:3.5);
\draw[blue,thick] (0,0) to[out=80,in=180] (5,6) to[out=0,in=95] (8,0);
\end{tikzpicture}
\end{document}