the axis of symmetry for the graph of the function $f(x)=3x^{2}+bx + 4$ is $x=\frac{3}{2}$. what is the…

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

For a quadratic function $y = ax^{2}+bx + c$, the axis of symmetry is given by $x=-\frac{b}{2a}$. In the function $f(x)=3x^{2}+bx + 4$, $a = 3$.

We know that $x=\frac{3}{2}$ and $a = 3$. Substituting into $x=-\frac{b}{2a}$, we get $\frac{3}{2}=-\frac{b}{2\times3}$.

Cross - multiply: $3\times(2\times3)=-2b$. So, $18=-2b$. Then, divide both sides by $- 2$: $b=-9$.

B. -9