Question

unit algebra: concepts and connections - aa07 quadratic functions: standard form the axis of symmetry for the graph of the function ( f(x) = \frac{1}{4}x^2 + bx + 10 ) is ( x = 0 ). what is the value of ( b )? options: ( 3 ), ( \frac{1}{2} ), ( -3 ), ( -12 )

Explanation:

Step1: Recall axis of symmetry formula

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

Step2: Identify given values

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

Step3: Substitute and solve for $b$

$6=-\frac{b}{2\times\frac{1}{4}}$
$6=-\frac{b}{\frac{1}{2}}$
$6=-2b$
$b=\frac{6}{-2}=-3$

Answer:

$-3$