Final answer:
The question is about a quadratic equation in vertex form, which doesn't directly calculate a product of values, but changing it into standard form would allow for finding roots to theoretically calculate their product.
Step-by-step explanation:
The student's question is about finding the product of the values obtained from a quadratic equation given in vertex form f(x) = -(1/3)(x+2)² + 7. However, the question seems to be about understanding the vertex form itself rather than finding the product of roots, because a quadratic equation in vertex form isn't directly about products of numbers.
Nevertheless, converting the provided expression to a standard quadratic equation would allow us to find the x-intercepts (if they exist) and then determine the product of those values. The vertex form of a quadratic equation is f(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola, and 'a' affects the width and direction of the parabola. If we wanted to find the x-intercepts or 'roots' of the quadratic equation from the vertex form, we would set f(x) to zero and solve for x.