Final answer:
The x-coordinate of the parabola's vertex for the equation y = (x - 6)(x + 12) is -3, which is the midpoint between the roots of the equation.Option B is the correct answer.
Step-by-step explanation:
The x-coordinate of the vertex of the parabola defined by the equation y = (x - 6)(x + 12) can be found by using the fact that the vertex form of a quadratic function is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In this case, the x-coordinate of the vertex is at the midpoint between the roots x = 6 and x = -12 because a parabola is symmetrical. To find the midpoint, we use the average of the two x-values, which is (6 + (-12))/2 = -3. So, the x-coordinate of the parabola's vertex is -3.
The x-coordinate of the vertex of the given parabola, y = (x - 6)(x + 12), can be determined by leveraging the symmetry of the parabola. The vertex form y = a(x - h)^2 + k implies the vertex is at (h, k). As the parabola is symmetrical, the x-coordinate of the vertex is the midpoint between its roots. By averaging the roots, (6 + (-12))/2, we obtain -3 as the x-coordinate of the vertex. This method efficiently exploits the symmetry of the parabolic shape, providing a straightforward means to identify the vertex's x-coordinate without explicitly solving the quadratic equation or completing the square.