Suppose you have ordered one medium onion ring and one 16oz chocolate shake from Burger King. The onion rings have 19 grams of fat and the shake has 23
grams of fat. If each cheeseburger has 13 grams of fat, how many cheeseburgers
can you order and still keep the total fat content of the meal to no more than 81
grams?

What is the equation/inequality for the situation?

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.

8: 40

2 hours

10: 40

55 min

11: 35