Answer:
b = -3
Step-by-step explanation:
f(x)=1/4x²+ bx+ 10
The axis of symmetry is equal to the x-coordinate of the vertex
The vertex is the point (h,k)
The equation of the axis of symmetry is given as
y = a( x - p )²+ q
x - p = x - h
h = x
x = 6, therefore, h = 6
So, we solve the quadratic equation
f(x) - 10= 1/4x²+ bx
f(x) - 10 = 1/4(x² + 4bx)
To be able to properly solve the quadratic equation, we would be using using completing the square method
f(x) - 10 + b² = 1/4(x² + 4bx + 4b²)
f(x) +(b² - 10) = 1/4(x+ 2b²)
f(x) = 1/4(x+ 2b²) - (b² - 10) ........1
Remember,
The equation of the axis of symmetry is given as
y = a( x - p )²+ q
x - p = x - h
h = x
If x = 6, therefore, h = 6 also
Since h = 6, we substitute.
x + 2b = (x - 6)
2b = - 6
b = -6/2
b = - 3
