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…

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 value of $b$?\n-12\n-3\n$\\frac{1}{2}$\n3

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 value of $b$?\n-12\n-3\n$\\frac{1}{2}$\n3

Answer

Explanation:

Step1: Recall axis of symmetry formula

For quadratic $f(x)=ax^2+bx+c$, axis is $x=-\frac{b}{2a}$

Step2: Identify given values

$a=\frac{1}{4}$, axis $x=6$

Step3: Substitute into formula

$6 = -\frac{b}{2\times\frac{1}{4}}$

Step4: Simplify denominator

$6 = -\frac{b}{\frac{1}{2}}$ which is $6 = -2b$

Step5: Solve for b

$b = \frac{6}{-2} = -3$

Answer:

-3