for [tex]f(x)=ax^2+bx+c[/tex], the axis of symmetry is [tex]x=\frac{-b}{2a}[/tex]
given that axis of symmetry is x=6, [tex]\frac{-b}{2a}=6[/tex]
we know that a=1/4 from the problem, so
[tex]6=\frac{-b}{2(\frac{1}{4})}[/tex]
[tex]6=\frac{-b}{\frac{1}{2}}[/tex]
[tex]6=-2b[/tex]
divide by -2 both sides
[tex]-3=b[/tex]
the value of b is -3
