The quadratic equation y = -6.1? + 100.X - 180 models the store's daily profit, y, for selling soccer
balls at x dollars.
The quadratic equation y = -412 + 80.X – 150
models the store's daily profit, y, for selling
footballs at r dollars. Use a graphing calculator to
find the intersection point(s) of the graphs, and
explain what they mean in the context of the
problem.

(TIMED QUESTION)

the correct answer is c

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.