The value of b is -3
Explanation:
The function is
and ![x=6](https://tex.z-dn.net/?f=x%3D6)
The function is of the form ![y=a x^{2}+bx+c](https://tex.z-dn.net/?f=y%3Da%20x%5E%7B2%7D%2Bbx%2Bc)
where
,
and ![c=10](https://tex.z-dn.net/?f=c%3D10)
Using the axis of symmetry formula, we can determine the value of b.
Thus, the axis of symmetry formula is given by,
![x=\frac{-b}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%7D%7B2a%7D)
Substituting the values, we have,
![6=-\frac{b}{2(\frac{1}{4}) }](https://tex.z-dn.net/?f=6%3D-%5Cfrac%7Bb%7D%7B2%28%5Cfrac%7B1%7D%7B4%7D%29%20%7D)
Multiplying the denominator, we get,
![6=-\frac{b}{\frac{1}{2} }](https://tex.z-dn.net/?f=6%3D-%5Cfrac%7Bb%7D%7B%5Cfrac%7B1%7D%7B2%7D%20%7D)
Dividing, we get,
![6=-2b](https://tex.z-dn.net/?f=6%3D-2b)
Dividing both sides by -2, we get,
![-3=b](https://tex.z-dn.net/?f=-3%3Db)
Hence, the value of b is -3.