Answer:
b = -9
Step-by-step explanation:
Axis of symmetry of a parabola = -b / 2a.
Where y = ax² + bx + c.
Given f(x) = 3x^2 + bx + 4,
a = 3, and c = 4.
If the axis of symmetry is 3/2, than b can be found by substitution and algebra.
[ x = -b / 2a ] → [ 3 / 2 = -b / 2a ] →
[ 3 / 2 = -b / 2 (3) ] → [ 3 / 2 = -b / 6 ] →
[ 3 / 2 × 6 = -b / 6 × 6 ] → [ 18 / 2 = -b ] →
[ 9 = -b ] → [ -b = 9 ] → [ (-)(-b) = (-)(9) ] →
b = -9
