Describe the translation y= (x-2) squared +5 -> y = (x+2) squared - 3

9514 1404 393

  A.  T<-4, -8>

Step-by-step explanation:

To get the second equation, we had to replace x with x+4 (a translation left 4) and we had to add -8 to the function value (a translation down 8).

Left 4 and down 8 is the translation ...

  T<-4, -8>

answer:

24pi or letter 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.