What is the value of the x-coordinate of the vertex of the function shown below f(x)=(x+2)(x-6)

The roots of the quadratic function are x = -2 and 6. These are the x values where the graph crosses the x axis. Since the line of symmetry is the vertical line at the vertex, these roots are equal distances from the vertex.

6 - (-2) = 8

The roots are 8 apart, so the vertex is 4 away from both of them.

-2 + 4 = 2
6 - 4 = 2

The vertex is at x = 2