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

Answer:

$r = 16$, $s = -48$

Step-by-step explanation:

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

$f(x) = 3\cdot x^{2} - 24\cdot x + \frac{1}{3}$

$f(x) = 3\cdot (x^{2} - 8\cdot x) + \frac{1}{3}$

$f(x) = 3\cdot (x^{2} - 8\cdot x + 16 - 16) + \frac{1}{3}$

$f(x) = 3\cdot (x^{2}-8\cdot x + 16) + \frac{1}{3} - 48$

By comparing each expression, the results are presented below:

$r = 16$, $s = -48$