The axis of symmetry for the graph of the function is f(x) = 1/4x2 bx 10 is x = 6. what is the value of b?

we have

This is a vertical parabola open upward

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

In this problem

so the x-coordinate of the vertex is

Convert the quadratic equation in vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Factor the leading coefficient

Complete the square. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

remember that

so

substitute in the equation

therefore

the answer is