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…
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 $b$?\n-18\n-9\n9\n18
Answer
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
$a=3$, $x=\frac{3}{2}$, so $\frac{3}{2}=-\frac{b}{2(3)}$
Step3: Solve for b
Multiply both sides by 6: $3\times3=-b$ → $9=-b$ → $b=-9$
Answer:
-9