Answer:
The value of b is -9.
Step-by-step explanation:
We are given a equation as:
\(f(x)=\frac{3}{4}+3x^2+bx+4\)
\(f(x)=3x^2+bx+\frac{19}{4}\)
clearly the graph of this function will be a parabola.
for any quadratic equation of the type \(f(x)=ax^2+bx+c\)
the equation of axis of symmetry is given by:
\(x=\frac{-b}{2a}\) , here a=3 and b=b
also we are given axis of symmetry as \(x=\frac{3}{2}\)
that means \(\frac{-b}{2\times3}=\frac{3}{2}\)
\(b=-9\)
