A census report on the income of Americans says that with 95% confidence the median income of all U. S. households is $49,841 to $50,625. The point estimate (center of the interval) and margin of error for this interval are: a) Point estimate = $50,233: Margin of Error = $392
b) Point estimate = $50,625: Margin of Error = $392
c) Point estimate = $49,841: Margin of Error = $784
d) Point estimate = $50,233: Margin of Error = $784

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.

-1

step-by-step explanation: