Question

the first steps in writing $f(x)=3x^{2}-24x+10$ in vertex form are shown.
$f(x)=3(x^{2}-8x)+10$
$left(\frac{-8}{2}\
ight)^{2}=16$
what is the function written in vertex form?
$\bigcirc$ $f(x)=3(x + 4)^{2}-6$
$\bigcirc$ $f(x)=3(x + 4)^{2}-38$
$\bigcirc$ $f(x)=3(x - 4)^{2}-6$
$\bigcirc$ $f(x)=3(x - 4)^{2}-38$

Explanation:

Step1: Add/subtract the squared term

$f(x) = 3(x^2 - 8x + 16 - 16) + 10$

Step2: Rewrite grouped terms

$f(x) = 3((x - 4)^2 - 16) + 10$

Step3: Distribute the 3

$f(x) = 3(x - 4)^2 - 48 + 10$

Step4: Combine constant terms

$f(x) = 3(x - 4)^2 - 38$

Answer:

D. $f(x) = 3(x - 4)^2 - 38$