Question

Skateboard Revenue: A skateboard shop sells about 50 skateboards per week for the price advertised. For each $1 decrease in price, about 1 more skateboard per week is sold. The shop's revenue can be modeled by y=(70-x) (50+x). Use vertex form to find how the shop can maximize weekly revenue.

[I can get this into vertex form, but I'm not understanding how to read the vertex form of the equation to answer the question]

Answer 1

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.