Final answer:
The x-coordinate of a parabola's vertex can be found using the formula: x = -b/2a, where a and b are coefficients of the quadratic equation representing the parabola in the form ax^2 + bx + c = 0. Since the parabola intersects the x-axis at x=3 and x=9, we know that these are the two x-intercepts of the parabola. Therefore, the x-coordinate of the parabola's vertex can be found by taking the average of the x-intercepts: (3 + 9)/2 = 6.
Step-by-step explanation:
The x-coordinate of a parabola's vertex can be found using the formula: x = -b/2a, where a and b are coefficients of the quadratic equation representing the parabola in the form ax^2 + bx + c = 0.
Since the parabola intersects the x-axis at x=3 and x=9, we know that these are the two x-intercepts of the parabola. Thus, the solutions to the quadratic equation are x=3 and x=9.
Therefore, the x-coordinate of the parabola's vertex can be found by taking the average of the x-intercepts: (3 + 9)/2 = 6.