Since the parabola has a horizontal tangent line at the point (3/2,4/3), it means 

that this point (3/2,4/3) is the vertex of the parabola.


Hence, the parabola has the form


    y(x) = ,


where "a" is a coefficient (real number), now unknown.


To find "a", use the fact that the plot of the parabola passes through the point (0,-6). It means that


    y(0) = -6,   or    = -6,   or


     = -6.


It gives


     =  =  = ,


hence


    a =  = .


Thus the equation of the parabola is  


    y(x) = .


You can transform it to any other equivalent form you wish.


Regarding the plot, do it on your own.


You may use free of charge plotting tools from the Internet.