Final answer:
To maximize weekly revenue, the shop should sell skateboards at a price of $10 with a maximum revenue of $3500.
Step-by-step explanation:
The vertex form of a quadratic equation is given by y = a(x-h)² + k, where (h, k) represents the coordinates of the vertex.
In the given equation y = (70-x)(50+x), we can expand and rearrange to obtain y = -x² + 20x + 3500.
Comparing this with the vertex form, we can identify that a = -1, h = 10, and k = 3500.
The vertex form indicates that the vertex is located at the point (h, k). Therefore, the shop can maximize its weekly revenue by selling skateboards at a price of $10 (at x = 10) with a maximum revenue of $3500.