Answer:
[tex]b=-3[/tex]
Step-by-step explanation:
The given function is [tex]f(x)=\frac{1}{4}x^2+bx+10[/tex].
When we compare to [tex]ax^2+bx+=0[/tex], we have
[tex]a=\frac{1}{4}[/tex] and c=10
The equation of the axis of symmetry of a vertical parabola is:
[tex]x=-\frac{b}{2a}[/tex]
Also from the question the axis of symmetry is x=6
We substitute the values to get:
[tex]6=-\frac{b}{2*\frac{1}{4}}[/tex]
[tex]6=-\frac{b}{\frac{1}{2}}[/tex]
[tex]b=-\frac{1}{2}*6[/tex]
[tex]b=-3[/tex]
