The value of b is -3.
Axis of symmetry is a line that divides an object into two halves,thereby creation a mirror like reflection of either side of the object.
Now the given function is,
f(x) = 1/4 x^2 bx + 10
and axis of symmetry is at x = 6
Now the quadratic function in standard form is given as,
f(x) = a x^2 bx + c
By comprison we get,
a = 1/4
c = 10
Since axis of symmetry is a vertical line
x = -b/2a
Therefore,
6 = -b/2*(1/4)
-b = 6*2*(1/4)
or, b = -12/4
or, b = -3
Hence,The value of b is -3.
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