Question

the first steps in writing $f(x) = 4x^2 + 48x + 10$ in vertex form are shown.
$f(x) = 4(x^2 + 12x) + 10$
$left(\frac{12}{2}\
ight)^2 = 36$
what is the function written in vertex form?
$f(x) = 4(x + 6)^2 + 154$
$f(x) = 4(x + 6)^2 + 10$
$f(x) = 4(x + 6)^2 - 26$

Explanation:

Step1: Add/subtract the squared term

$f(x)=4(x^2+12x+36-36)+10$

Step2: Rewrite as perfect square

$f(x)=4((x+6)^2-36)+10$

Step3: Distribute the 4

$f(x)=4(x+6)^2 - 4\times36 + 10$

Step4: Calculate constant term

$f(x)=4(x+6)^2 - 144 + 10 = 4(x+6)^2 - 134$
(Note: The visible option matching this result is the bottom partial option $f(x)=4(x+6)^2 - 134$; the third option has a calculation error, the correct constant is -134)

Answer:

$f(x)=4(x+6)^2 - 134$ (the bottom partial option in the image)