"equation of a parabola with vertex (2,3)" is


    y = a*(x-2)^2 + 3,


where "a" is an unknown coefficient, which should be found.


"passing through (1.5,4)"  means


    4 = a*(1.5-2)^2 + 3,


which is the same as


    4 = a*(-0.5)^2 + 3

    4 - 3 = a*0.25

    1     = 0.25a

    a =  = 4.


So, the final equation of the parabola is  y = 4*(x-2)^2 + 3.