Question

The axis of symmerty for the graph of the function f(x) = 1/4x^2 + bc +10 is x=6 what is the value of b

Answer 1

Completing the square gives

`\frac14x^2+bx+10=\frac14(x^2+4bx+40)=\frac14(x^2+4bx+4b^2+40-4b^2)`

`\implies\frac14x^2+bx+10=\frac14(x+2b)^2+10-b^2`

At the point on the graph along the axis of symmetry, the squared term vanishes, so that when
`x=6`, we have
`x+2b=0`. So

`6+2b=0\implies 2b=-6\implies\boxed{b=-3}`