Question

the axis of symmetry for the graph of the function f(x)=3x²+bx+4 is x = \frac{3}{2}. what is the value of b? \bigcirc -18 \bigcirc -9 \bigcirc 9 \bigcirc 18

Explanation:

Step1: Recall axis of symmetry formula

For a quadratic function \( f(x) = ax^2 + bx + c \), the axis of symmetry is \( x = -\frac{b}{2a} \).

Step2: Identify \( a \) and substitute \( x \)

Here, \( a = 3 \) and \( x = \frac{3}{2} \). Substitute into the formula: \( \frac{3}{2} = -\frac{b}{2\times3} \).

Step3: Solve for \( b \)

Simplify the right - hand side: \( \frac{3}{2} = -\frac{b}{6} \).
Multiply both sides by 6: \( 6\times\frac{3}{2}= - b \).
Calculate \( 6\times\frac{3}{2}=9 \), so \( 9 = - b \), then \( b=-9 \).

Answer:

\( b = - 9 \) (corresponding to the option -9)