Express the function 'f' in standard form:

-2x^2 - 6x + 3

I've got:

(-2x^2 - 6x/2 + 36/4) + 3

(-2x^2 - 3x + 9) + 3

-2(x^2 - 3x/-2 + 9/-2) + 3 - (9/-2)

=y=(x + 3/2)^2 + 15/2

I inputted the original function and the standard form into a graphing calculator and it came up with two different parabolas. Did I make an error in my math?