we know that
the equation of a vertical parabola into vertex form is equal to
[tex]y=a(x-h)^{2} +k[/tex]
where
(h,k)-------> is the vertex of the parabola
if [tex]a > 0[/tex] -------> the parabola open upwards
if [tex]a < 0[/tex] -------> the parabola open downwards
case A) [tex]y=-3x^{2}[/tex]
[tex]a =-3[/tex]
so
[tex]a < 0[/tex] -------> the parabola open downwards
the vertex is the point [tex](0,0)[/tex] ------> is a maximum
therefore
[tex]y=-3x^{2}[/tex] open downwards
case B) [tex]y=(x-3)^{2}[/tex]
[tex]a =1[/tex]
so
[tex]a > 0[/tex] -------> the parabola open upwards
the vertex is the point [tex](3,0)[/tex] --------> is a minimum
therefore
[tex]y=(x-3)^{2}[/tex] open upwards
case C) [tex]y=x^{2}-3[/tex]
[tex]a =1[/tex]
so
[tex]a > 0[/tex] -------> the parabola open upwards
the vertex is the point [tex](0,-3)[/tex] --------> is a minimum
therefore
[tex]y=x^{2}-3[/tex] open upwards
therefore
the answer is
[tex]y=-3x^{2}[/tex] open downwards
