Question

HELP ASAP!!!

The volunteers at a high school football team’s concession stand are trying to decide on the price of the hot dogs they are selling. When they charge $2 for a hot dog, they sell an average of 70 hot dogs per game. With every $1 increase in the price, the number of hot dogs sold per game decreases by 8.

The volunteers can calculate the revenue earned from selling the hot dogs at each game using the expression -8x2 + 54x + 140, where x is the number of $1 increases in price.

What is the constant term in the polynomial expression, and what does it represent?

Answer 1

The constant is 140 and it represent the minimum amount of money they'll make from selling hotdogs when the price is not raised.

Explanation:

You're given the equation

y = -8x² + 54x + 140

The result from calculating the equation will give you how much money they made at the end of the day. And x is the amount of $1 price increase they had on the hotdog.

So we assume that they didn't raise the hotdog price at all (so x=0), then we would get:

y = -8(0)² + 54(0) + 140

y = 0 + 0 + 140

y = 140

Read further if you want more explanation...

So if they didn't increase their price at all, they would make at least $140.

Now lets plug in x=1 for a $1 increase in price.

we get

y = -8(1)² + 54(1) + 140

y = 186

ok, we see that the amount of money they made increased to $186 when they raise the price.

Now lets check when we raise the price by $2 (x=2)

y = -8(2)² + 54(2) + 140

y = 216

ok, now the revenue increased to $216

Just one last check, lets see what happen when we raise the price by $3 (x=3)

y = -8(3)² + 54(3) + 140

y = 230

Price increased again to $230.

As you can see, the 140 represent the revenue they make when the price is not raised at all (x=0).