Final answer:
The x-coordinate of the vertex of the graph y=(x+1)(x+5) is -3, which is determined by calculating the axis of symmetry between the two x-intercepts of the parabola.
Step-by-step explanation:
The x-coordinate of the vertex of the graph representing y=(x+1)(x+5) can be found using the vertex form of a quadratic equation or by calculating the axis of symmetry. The function y=(x+1)(x+5) is a quadratic equation in its factored form. To find the vertex, we need to identify the axis of symmetry, which is equidistant from the x-intercepts (roots) of the parabola. Since the x-intercepts are at x=-1 and x=-5, the axis of symmetry is the average of these two values. Thus, x = (-1 + (-5)) / 2 = -6 / 2 = -3. Therefore, the x-coordinate of the vertex is -3.