Question

A soccer team is selling t-shirts as a fundraiser. The table shows the number of t-shirts they can expect to sell depends on the x, the price of each t-shirt.%0D%0A%0D%0AExpected T-Shirt Sales%0D%0A%0D%0APrice per t-shirt (x dollars)%0D%0A%0D%0ATotal Cost (y dollars)%0D%0A%0D%0A8%0D%0A%0D%0A800%0D%0A%0D%0A9%0D%0A%0D%0A855%0D%0A%0D%0A10%0D%0A%0D%0A900%0D%0A%0D%0A11%0D%0A%0D%0A935%0D%0A%0D%0A12%0D%0A%0D%0A960%0D%0A%0D%0A13%0D%0A%0D%0A975%0D%0A%0D%0A14%0D%0A%0D%0A980%0D%0A%0D%0A15%0D%0A%0D%0A975%0D%0A%0D%0A16%0D%0A%0D%0A960%0D%0A%0D%0AWhich equation describes the relationship between the total number of dollars in t-shirt sales, y, and the price per t-shirt, x?

Answer 1

The data fit a downward parabola with vertex at (14, 980). Using vertex form:

y = a(x − 14)^2 + 980.

Plugging in (8, 800) gives 800 = a(8−14)^2 + 980 → a = −5. So

y = −5(x − 14)^2 + 980,

which expands to

y = −5x^2 + 140x.