f(x)=-3(x+1/2)^2+1/2
I haven't actually solved anything - there is nothing to solve. I have just simplified.
$$\\f(x)=-3(x+0.5)^2+0.5\\\\
f(x)=-3[(x+0.5)^2]+0.5\\\\
f(x)=-3[x^2+x+0.25]+0.5\\\\
f(x)=[-3x^2-3x+0.75]+0.5\\\\
f(x)=-3x^2-3x+0.75+0.5\\\\
f(x)=-3x^2-3x+1.25\\\\$$