Answer:
The correct option is;
B) -6
Step-by-step explanation:
The given parameters are;
The line of symmetry of f(x) = The line of the reflection of g(x) over the y-axis
f(x) = 3·x² + b·x + c
From the given graph of g(x), we have;
The vertex point of g(x) = (-1, 8)
The line of symmetry is the line x = -1
The image of the reflection of (x, y) over the y-axis is (-x, y)
The image of the vertex of g(x) following a reflection across the y-axis is (1, 8)
Therefore;
The line of symmetry of the image of g(x) following a reflection over the x-axis is the line x = 1
The line (axis) of symmetry of a quadratic function is the line x = -b/(2·a), which is a line that always go through the vertex of the parabola
Where;
a = The coefficient of x²
b = The coefficient of 'x'
For f(x) = 3·x² + b·x + c, a = 3, and b = b
Given that f(x) and the image of g(x) have the same line of symmetry, we have;
The line of symmetry of f(x) is x = 1
Therefore, from the formula for the line of symmetry, we have;
x = -b/(2·a)
x = 1
By substitution, we have;
1 = -b/(2·a)
∴ -2·a = b
Given that a = 3, we get;
-2 × 3 = -6 = b
b = -6
lies between the two consecutive numbers 3 and 4.