Frederick and Fabricio enjoy catching Pokémon every day. They have developed different techniques of catching as many Pokémon as possible in an hour. Frederick represented the results of his catching techniques in the graph below, where the x-axis represents the time in hours and the y-axis represents the number of Pokémon in his pokeballs, while Fabricio decided to represent his results as the function f(t)=15t. After how many hours would Frederick have more Pokémon than Fabricio?

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0

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.

think the answer is 30 degrees. if not than it is 20 degrees. not 100% sure. let me know if it was right.

gill russ