In the function f(x) = 3(x2 − 8x + ) + 9, what number belongs in the blank to complete the square?

The number that belongs to the blank is 16

Explanation:

The given function is f(x) = 3(x² − 8x + ____) + 9

We need to determine the number that belongs to the blank.

The number can be determined by completing the square.

The middle term is 8

The last term can be determined by dividing the middle term by 2 and then squaring the term.

Thus, we have,

Squaring the term, we get,

Thus, the number that belongs to the blank is 16.