Rick has thrown for 1,244 yards in just six games this season. The single season passing record at St. Pius XIII High School l is 2277 yards played over the course of 15 games. If Rick has 9 games left in this football season, how many yards must he average per game to break the single season passing record?

Step-by-step explanation:

The daily profit can be +, 0 or -.  The zeros of this function are the points at which the graph crosses the x-axis and, moreover, the x-values at which the profit is zero.  These x-values represent prices of a hot dog in dollars.

To find these zeros, we set the function y = -2(x-3)^2+4 equal to zero and solve for x:

0 = -2(x-3)^2+4

Dividing both sides by -2, we get 0 = (x - 3)^2 - 2.

Rewriting this result, (x-3)^2 = 2.

Taking the square root of both sides:  x - 3 = plus or minus √2.

Then x = 3 plus or minus √2, or x = 3 + √2 and x = 3 - √2, which have the values 4.414 and 1.586.

The zeros of this function are $1.58 and $4.41.  The significance of these two dollar amounts is that the daily profit is zero at each of these two values.  The profit is positive for the price range $1.58 to $4.41.