Abiologist studied the populations of black bear and brown bears over a 10-year period. the biologist modeled the populations, in thousands, with the following polynomials where x is time, in years. black bears: 2.3x2 – 5.6x + 2.3brown bears: 2.4x2 + 7.2x + 0.97what polynomial models the total number of brown and black bears?
a. 4.7x^2 + 1.6x + 3.27
b. 4.7x^2 – 1.6x – 3.37
c. 4.7x^2 + 1.6x – 3.37
d.4.7x^2 – 1.6x + 3.37

y/x=18

step-by-step explanation:

answer: translate the circles so they share a common center point and dilate circle y by a scale factor of 3.

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.