Answer:
b = -9
Step-by-step explanation:
If we have a function with the form:
[tex]f(x)=ax^2+bx+c[/tex]
The axis of symmetry is equal to:
[tex]x = \frac{-b}{2a}[/tex]
So, for the function [tex]f(x)=3x^2+bx+4[/tex], the value of a is 3 and the value of c is 4. It means that its axis of symmetry is equal to:
[tex]x=\frac{-b}{2(3)}=\frac{-b}{6}[/tex]
Solving for b, we get that: [tex]b=-6x[/tex]
Additionally, the axis of symmetry is [tex]x=3/2[/tex], so replacing x by 3/2, we get that b is equal to:
[tex]b=-6(3/2)\\b=-9[/tex]
