The first steps in writing f (x) = 3x2 - 24x + 10 in vertex form are shown.

f (x) = 3 (x2 - 8x) + 10

(-8/2) ^2 = 16

What is the function written in vertex form?

A. f (x) = 3 (x + 4) 2 - 6

B. f (x) = 3 (x + 4) 2 - 38

C. f (x) = 3 (x - 4) 2 - 6

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

The vertex form has the general form of:

y = a (x-h) ^2 + k

We have the given equation:

f (x) = 3x^2 - 24x + 10

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

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

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

Then, the correct answer is D.

Following the steps already shown to transform the given function into the vertex form, we have:

f (x) = 3 (x2 - 8x + 16) + 10 - 3 (16)

f (x) = 3 (x - 4) (x - 4) + 10 - 48

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

Therefore, the function written in vertex form is:

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