the axis of symmetry for the graph of the function $f(x)=\frac{1}{4}x^{2}+bx + 10$ is $x = 6$. what is the…

Answer:

A. - 3

Explanation:

Step1: Recall axis - of - symmetry formula

For a quadratic function $y = ax^{2}+bx + c$, the axis of symmetry is given by $x=-\frac{b}{2a}$. In the function $f(x)=\frac{1}{4}x^{2}+bx + 10$, $a = \frac{1}{4}$ and $c = 10$.

Step2: Substitute values into formula

Since the axis of symmetry $x = 6$, we substitute $x = 6$ and $a=\frac{1}{4}$ into $x=-\frac{b}{2a}$. So, $6=-\frac{b}{2\times\frac{1}{4}}$.

Step3: Simplify the right - hand side

First, simplify $2\times\frac{1}{4}=\frac{1}{2}$. Then the equation becomes $6 =-\frac{b}{\frac{1}{2}}$, which is equivalent to $6=-2b$.

Step4: Solve for $b$

Divide both sides of the equation $6=-2b$ by $- 2$. We get $b=-3$.