Question

The axis of symmetry for the graph of the function f(x)=1/4^2+bx+10 is x=6. What is the value of b?

Answer 1

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