Final answer:
The statement about finding the vertex form of a quadratic equation by plugging in the solution of a system of equations is FALSE, as a solution does not provide enough details unless the solution is at the vertex or helps determine the value of 'a'.
Step-by-step explanation:
The statement "If (x, y) is the solution of the system of equations, then plugging in the vertex and another point will yield the vertex form" appears to be based on some confusion. The vertex form of a quadratic equation is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola. To write a quadratic equation in vertex form, you need the vertex (h, k) and one other point (x, y) on the parabola to determine the value of a. However, a solution (x, y) to a system of equations does not provide enough information to determine the vertex form of a quadratic equation unless one of those equations is quadratic and the solution coincides with its vertex or provides sufficient information to determine a. Therefore, the statement is False.