Question 1178870
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As the problem is worded,  printed,  posted and presented,  there are  INFINITELY  MANY  quadratic functions with the pre-assigned vertex.



They all have the form / (an equation)


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


where  "a"  is an arbitrary non-zero real number.



So,  NETHER  the original post is formulated correctly,  NOR  the answer by  @MathLover1 is correct.




            To be totally clear,   they   B O T H    are   I N C O R R E C T.