Question

unit algebra: concepts and connections - aaa07 quadratic functions: standard form the axis of symmetry for the graph of the function $f(x) = 3x^2 + bx + 4$ is $x = \frac{3}{2}$. what is the value of $b$? options: 18, -18, -9, 9

Explanation:

Step1: Recall axis of symmetry formula

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

Step2: Substitute known values

Given $a=3$, $x=\frac{3}{2}$:
$\frac{3}{2}=-\frac{b}{2\times3}$

Step3: Solve for $b$

Multiply both sides by 6:
$3\times3=-b$
$9=-b$
$b=-9$

Answer:

-9