hello :
note : x = b/2a an equation for The axis of symmetry when f(x) =ax²+bx+c
in this exercice : 6 = (b)/(2)(1/4)
6=(b)/0.5
b = 3
anathor solution :
f(x) = (1/4)x² +3x +10 = (1/4)(x² +12x )+10 =(1/4)(x²-2(6)(x)+6²-6²)+10
f(x) = (1/4)(x-6)² +1.....(vertex form the vertex is : (6 . 1)