Final answer:
The vertex of the parabola represented by the equation f(x) = -2 (x-4)^2 - 7 is (4, -7), which is evident from the equation's vertex form.
Step-by-step explanation:
The vertex of a parabola represented by the equation f(x) = -2 (x-4)^2 - 7 can be found directly from the equation itself. This is because the equation is already in vertex form, which is f(x) = a(x-h)^2 + k, where (h, k) is the vertex of the parabola. For the given equation, the vertex is at (4, -7), corresponding to the values of h and k in the formula. Counting the number of parts that add up to $24 will give us the number of weeks Sarah needs to save. This model visually supports our equation and helps us solve for W. In this case, W equals 4 because 6 dollars times 4 weeks equals the 24 dollars needed for the art supplies.