Question

Sandy was given this function. f(x)=3x2−24+1/3 She used the method of completing the square to rewrite the function. In this second step of her process, r and s are real numbers. f(x)=3(x2−8x+r)+1/3+s What are the values of r and s? Enter your answers in the boxes.

Answer 1

`r = 16`,
`s = -48`

Explanation:

The values of
`r` and
`s` can be found with the help of algebraic manipulation on the second-order polynomial described on statement:

`f(x) = 3\cdot x^(2) - 24\cdot x + (1)/(3)`

`f(x) = 3\cdot (x^(2) - 8\cdot x) + (1)/(3)`

`f(x) = 3\cdot (x^(2) - 8\cdot x + 16 - 16) + (1)/(3)`

`f(x) = 3\cdot (x^(2)-8\cdot x + 16) + (1)/(3) - 48`

By comparing each expression, the results are presented below:

`r = 16`,
`s = -48`